DOCUMENT RESUME

ED 063 686 Eh 004 427

AUTHOR Golladay, Fredrick L,; And OthersTITLE Education and Distribution of Income4 Some

Exploratory Forays. Terlhnical Reports. Conference onPolicies tor Educationca Growth (Paris, France, June3-5, 1970).

INSTITUTION Organisation for Economic Cooperation andDevelopment, Paris (France).

PUB LATE 20 May 70NOTE 164p.; Related to Background Study No,

EDRS PRICEDESCRIPTORS

MF-$0.65 HC-$6.58Cost Effectiveness; *Education; *EducationalBenefits; *Educational Economics; EducationalFinance; *Educational Policy; Educational Research;Educational Sociology; Equal Education; HigherEducation; *Income; Investment

ABSTRACTThe first paper in this series, ',Problems in the

Econometric Analysis of Educational Technology, by Fredrick L.Golladay, examines the analogy between empirical production functionsin economic research and the school characteristic study. The secondpaper, ',Problems in Making Policy Inferences from the ColemanReport, by Glen Cain and Harold Watts, presents the theoreticalbases for causally interpretable Nultivariate empirical research intoeducation. The third paper, HEducdtion and Income: A Study ofCross-Sections and Cohorts,1 by Robinson Hollister, summarizesresearch into the problems of conceptualization and the measurementof school characteristics, inputs, and outputs. The fourth paper,',Patterns of Rates of Return to Investment in Education: SomeInternational Comparisons, by W. Lee Hansen, reviews briefly thestatistical problems that emerge in school characteristic studies.The final paper, oThe Search for Equity in the Provision and Financeof Higher Education,fl by W. Lee Hansen and Burton A. Weisbrod,summarizes the discussions and draws conclusions for the appropriatefocus of research into resource allocation to And within education.Related documents are ED 057 470 and EA 004 323. (Author)

DEPARTMENT OF HEALTH,EDUCATION & WELFAREOFFICE OF EDUCATION

THIS DOCUMENT HAS BUN REPRODUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIG.INATING IT POINTS OF VIEW OR OPIN.IONS STATED DO NOT NECESSARILYREPROSENT OFFICIAL OFFICE OF EDU.CATION POSITION OR POLICY

NCONFERENCE

ON POLICIES FOREDUCATIONAL GRowni

PARISI 315 JUNI 1970

1

EDUCATION AND DISTRIBUTIONOF INCOME

VII

cif TTTlnfinrurrin

ORGANISATION PON ECONOMIC CO.OPIRATION AND DIVELOPMENT PARIS 1971

F OREWORD

The 1970 Paris Conference on Policies for Educational Growth was organized by OECD as a sequelto Its 1901 Washington Conference on Economic Growth and Investment in Education, The purpose of theConference was to weigess tho nature and consequences of the expansion of education in OECD countriesduring the last lo 15 years and to rolViier the main policy problems arising from continued educationalgrowth in the fute.e.

The proeeedings of the Conference are presented in a set of eight volumes consisting of:

- The General Report of the Conference published under the title: EDUCATIONAL POLICIES FORTHE 1970,s ,

and the following series of documents containing the twelve supporting studies prepared by the Secretariat:

11 ED VCATIONA1, EXPANSMN IN OECD CO ITNTRI ES SINCE 1950 (Background Report No, I).III TRENDS IN EDCCATR)NAL EXPENDITURE IN OECD COUNTRIES SINCE 1950- (Background

Report No. 2).

rk, GROVP DISPARITIES IN EDUCATIONAL PARTICIPATION AND ACHIEVEMENT:

Group Disparities in Educational Participation - (Background Report No, 4),Differences in School Achievement and Occupational Opportunities - Explanatory Factors,A Survey based on European Experience - (Background Report No, 10),

V TEACHING RESOURCES AND STRUCTURAL CHANGE:

'reaching Staff and the Expansion of Education in Member Countries since 1950 (BackgroundReport No, 3),

Changes in Secondary and Higher Education - (Background Report No, 6),

Educational Technology: Practical Issues and Implications - (Background Report No, 7).VI THE DEVELOPMENT OF EDUCATIONAL PLANNING:

Educational Policies, Plans and Forecasts during the Nineteen-Sixtios and Seventies -(Background Report No, 5),

Educational Planning Methods - (Background Report No, 8),

The Role of Analysis In Educational Planning - (Background Report No, 9),VII EDUCATION AND DISTRIBUTION OF INCOME (Background Report No, 11),

viii AI.TERNATIVE EDUCATIONAL ITTURES IN THE UNITED STATES AND IN EUROPE:METHODS, ISSUES AND POLICY RELEVANCE (Background Report No, 12),

CONTENTS

TECHNICAL REPORTS RELATED TO BACKGROUND REPORT No. 11

"PERMISSION TO REPRODUCE THIS COPY.RIGHTED MATERIAL HAS BEEN GRANTEDSy

f0 urnir-6131171=T7111711ZUNDER AGREEMENTS WITH THEI U.S. OFFICEOP EDUCATION. PURTHER REPRODUCTIONOUT0011 THE ERIC SYSTEM REQUIRES PER.MISSION OP THE COPYRIGHT OWNER

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II

TECHNICAL REPORTS RELATED TO BACKGROUND REPORT No 11

Parir 1 Problems in the Econometric Analysis of Educational Technolngyby Fredrick L, Golladay 41

Paper 2 Problems in Making Policy Inferences from the Coleman Reportby Glen Cain and Harold Watts 67

Paper 3 Education and Income: A Study of Cross-Sections and Cohortsby Robinson Hollister 93

Paper 4 Patterns of Rates of Return to Investment in Education: Some InternationalComparisons

by W. Lee Hansen 163

Paper 5 The Search for Equity in the Provision and Finance of Higher Educationby W. Lee Hansen and Burton A, Weisbrod 201

CONTENTS

Paper 1

PROBLEMS IN THE ECONOMETRIC ANALYSIS OF EDUCATIONAL TECHNOLOGY

Introduct ion 43

- Produotion Function Estimation for Public Seotor Activities 45

Ii - Eduoational Theory and Empirical Produotin Function Estimation for Education 47

1:11 - Measurement and Conceptualization of Variables for Production FunctionEstimation 59

IV - Statistical Techniques for Production Function Estimatior. 63

V - Summary 65

Paper 2

PROBLEMS IN MAKING POLICY NFERENCES FROM THE COLEMAN REPORT

A General, introduction 69

I - Introduction 71

- Policy Objectives Underlying the Coleman Report 73

in - A Suggested Approach to Measuring the Determinants of EducationalAchievement 75

IV - Interpre1ng Spooifio Variables in the Coleman Report 87

V - Conclusion 91

38

Paper 3

EDUCATION AND INCOME: A STUDY OF CROSS-SECTIONS AND COHORTS

Introduction 913

I - The Dloision on Educational Investment 07

Ii - The 1939 to 1959 Experience 101

UI - The 1956 to 1966 Experience 127

IV - A Multi-Factor Model of 'rime-Series of Education-Income Relationships 137

V - Summary and Conclusions 149

Appendix A

Appendix B

- A Crude Method for Translating Ratios of Present Values intoRatios of Internal Rates of Return 153

- A Supply and Demand Equation Model for Age - Education - IncomeRelationships and Some Evaluation of its Coefficients 157

Paper 4

PATTERNS OF RATES OF RETURN TO INVESTMENT lN EDUCATION:SO ME INT ERNA TIONA L COMPARISON S

General Introduction 165

Introduoti on 167

The Rate of Return Approach 167

II Sample of Studies 171

Comparability inThe Nature of Internal. Rates of Return 175

Uses of Internal Rates of Return 175

Patterns of Rates of Return 176

Explanations of Rates of Return Patterns. 177

IV Association with Educational Distribution Data 181

V Conclusion 185

Appendix Tables A and B Patterns of Rates of Return to Investment in &button: SomeInternational Comparisons 188

References 197

Paper 5

THE SEARCH FOR EQUITY IN THE PROVISION AND FINANCE OP HIGHER EDUCATION

Introduction 203

I - Equity and Efficiency: Conceptual Issues 205

II - The Distribution of Costs and Direct Benefits of Public Higher Education: TheCase of California 2 11

Conclusion 22 1

-40

Paper 1

PROBLEMS IN THE ECONOMETRIC ANALYSISOF EDUCATIONAL TECHNOLOGY

by

Fredrick L. Golladay1

1, The author wishes to acknowledge the financial support of the Institute for Research on Poverty, University of Wisconsin, andthe Organisation for Economic Co-operation and Development. He also wishes to thank W. Lee Hansen, Robinson Hollister, LouisEmmerii and M. Vera DeVault for helpful comments on earlier drafts of the paper, Marilyn Hastings and Mary Alberston Golladby haveprovided considerable research assistance.

INTRODUCTION

The importance of education to various dimensions of national development and to individual welfarehas been thoroughly documented. However, to provide educational opportunities as abundantly as edu-cationists and social scientists would urge is beyond the economic resources of even the richest nation.Increasing the efficiency with which educational resources are allocated is therefore imperative.

A number of recent studies have attempted to provida insights into the educational process and intothe efficiency of resource allocation to and within education through multivariate statistical analyses ofdata drawn from schools and school systems. The ultimate objective of these studies has been to eval-uate the strength of causal relationships between school inputs and characteristics and student achieve-ment. Several scholars have challenged the findings of these studies; despite rather widespread criticismof school characteristics studies, it is apparent that the conclusions of these projects are influencingeducational policy. Not only have the results of these studies been cited as justification for policy re-garding resource allocation to and within educational systems, but attempts have also been made to dis-count criticisms of the studies. One well-known policy adviser has even suggested that the objectionsraised by critics are not legitimate but rather are attempts to preserve some cherished and long-heldpreconceptions regarding the educational process1.

The purpose of this paper is to provide a comprehensive, systematic examination of the theoretical,conceptual and empirical problems plaguing research into the educational process which is based uponextensive observational data. The goal of this discussion is to demonstrate that the shortcomings ofschool characteristics studies are so pervasive and fundamental as to tmdermine any confidence that onemight place in the findings of such research. An extensive critical literature has emerged which insomewhat fragmentary fashion has attacked aspects of particular studies; most of the discussion hasfocused upon empirical defects of the studies. This paper addresses a more basic issue - whether thelarge-scale, observational study of education is an appropriate research strategy for examining thetechnology of the educational process.

This paper is presented in five parts. Part I examines the analogy between empirical productionfunctions in economic research and the school characteristics study, Several scholartt- have explicitlydrawn the analogy and have borrowed heavily upon the more developed literature of production functionestimation in preparing research strategies, This discussion considers the implications of public pro-duction of educational services for the estimation and interpretation of production functions for educa-tion. Part II presents the theoretical bases for causally interpretable, multivariate empirical researchinto education, Observational studies require a well-developed, theoretical system in order to identifyrelevant variables and to suggest appropriate functional relationships among dependent and independentvariables, This part of the paper both reviews the need for theory in empirical research of the typebeing considered here and assesses the literature of educational theory in an attempt to construct anempirically relevant operational-theoretical model of the educational process. Part III summarizes

1, Daniel P. Moynihan, "Sources of Resistance to the Coleman Report", Liattard Educational 38, 1, 1968, pp, 23-36,

research into the problems of conceptualization and measurement of school characteristics, inputs andoutputs, Attention is focused upon the absence of well-scaled, operational measures of these variablesand the resulting iml.lications for analysis and lnterpretation of empirical relationships, Part IV brieflyreviews the statistical problems that emerge in school characteristics studies, Part V summarizes thediscussions and draws conclusions from the paper for the appropriate focus of research into resouvJeallocation to and within education,

It should be noted that each part of the paper has been presented as though the problems consideredin the other parts did not Nist, This has been done in order to simplify the discussions; the reader shouldbear in mind that the discussion of a problem which occurs whether or not other defects have been cor-rected does not imply that the author has dismissed the earlier defects.

1

PRODUCTION FUNCTION ESTIMATIONFOR PUBLIC SECTOR ACTIVITIES

The production function concept has been demonstrated to be a useful empirioal tool with which toderive insights into efficient responses of private firms to changes in factor or product prices. Severalscholars have suggested that application of production function concepts to the analysis of technical al-ternatives in public education would be fruitfull However, several critical assumptions employed inproduction function estimation are violated by public production activities. The purpose of this part isto indicate the nature of these assumptions and to underscore the consequences of their being violatedin studies of educational practices.

The useenlness of production functions in the study of the behaviour of private firms depends cru-cially on the assumption of maximizing behaviour. The assumption of profit maximization permits oneto assert that observed production techniques are efficient; the theory of the firm offers compellingevidence that enterprises which are not efficient in the economic sense will not survive the rigours ofcompetition. Economic efficiency, defined as minimization of the cost of production, in addition impliesthat techniques being employed are efficient in a more narrow physical or engineering sense. The vari-ations observed in technology may therefore be assumed to reflect optimal adjustments to changes ineconomic conditions, particularly regarding the cost of factor services and materials.

The assumption of profit maximization also implies that factors will be paid approximately theirmarginal contributions to output; this implication is important because it facilitates the aggregatAon ofheterogeneous inputs into production. The broad category of inputs denoted as labour may be usefullyanalysed by a single dimensional index expressed as dollars worth of labour productivity, if one mayassume that marginal productivity theory is appropriate. In the absence of this highly useful implica-tin* of maximizing behaviour,, one is forced to regard every distinguishable skill as an input to beanalysed explicitly.

It is perhaps obvious that the implications of technical efficiency and consistent aggregation of inputsderived from the assumption of maximizing behaviour are not appropriate to studies of production in thepublic sector generally. This conclusion is particularly important to research into educational technolo-gy based upon observational data.

Educational decision makers do not appear to maximize any well-defined criteria function. Puristsmay argue that eduoational decisions, if rational and consistent, must reflect some underlying set ofobjectives which are being optimized, at least implicitly. One may concede this point, yet recognizethat the decentralized structure of educational systems creates a presumption that the latent decisionfunctions of teachers, school administrators and public officials are likely to be highly diverse. The

1, For example, see Samuel S. Bowles, "Towards An Educational Production Function", in NatIon4l Uurepu of Sao o icResearch Conference on Income and Wealth, New York, 1908,

observed technical choices may be optimal with respeot to an almost infinite variety of objectives, andthere is no reason to expect these objeotives to be mutually consistent or reinforcing.

The absence of a well-defined objective function which is being maximized by educational deoisionmakers destroys the implication of produotion theory, that observed technologies are efficient in anengineering sense, Ono cannot argue that observed techniques are efficient methods for obtaining aparticular output where even the output being maximized is ambiguous,

The second implioation of profit maximizing behaviour, that marginal productivity theory explainspayments to factors, is also inappropriate to education, The highly convenient procedure of aggregatinginputs by values assigned by the market is therefore not legitimate, It may be argued that the opportunitycost of remaining in the teaohing profession is determined by market foroes; profit maximizing firmshave determined the value of a teacher as a produotion worker, This sugpsts, however, only that alower bound on the value of a teaoher is established; even this value would appear to have little relevanceto one's produotivity as a teacher, The widespread use of salary schedules, seniority inorements andthe reluctance to employ "merit" salary payments reinforces the view that marginal productivity theoryis not an adequate conceptualization of wage determination in education,

Similar arguments demonstrating the inappropriateness of aggregating inputs by using market valu-ation may be made for classes of educational inputs other than teachers, There is no a priori, basis forthe view that the value of educational resources bears any oonsistent relationship to a well-defined, gen-eral index of school outputs, For example, "lavish athletic facilities may contribute to a oommunity'ssense of prestige without having any positive impact on student reading ability. Educational inputs musttherefore be considered in a highly detailed and disaggregative fashion if one is to capture the variabilityin school inputs,

Implicit in muoh of the above criticism of production function estimation is the realization that throutputs of formal education are as elusive as school inputs, The issue of school decision-making mightbe reintertweted as an examination of the question, "What do schools produce?", Beoause education istypically provided publioly without direct charge, it is impossible to infer a well-defined, general indexof school outputs, The outputs of many industries are equally diverse; however the marketing of thesegoOds provides a rigorous evaluation of the social values attached to these goods, permitting one toestimate a single dimensional measure of production, In short, market prices may be used as aggre-gation weights for related but heterogeneous outputs. A community's preferences for advanoed plaoe-ment physics education, remedial reading instruction and inter-school athletics are never subjected tothese rigours of market evaluation.

This part of the paper has attempted to demonstrate that empirical production functions for edu-cation estimated from observational data confront important problems because of the nature of publicsector activities, The interpretation of the estimated production function for education as a summar-ization of technically efficient alternatives is destroyed by the absence of consistent maximizing behaviour;the estimated function summarizes a variety of often unrelated production activities, In addition, thereis no theoretical basis for the assumption that the estimated relationships are in any sense technicallyefficient, Finally, the absence of an elegant theoretical justification for aggregation of either schoolinputs or outputs considerably complicates the study of educational technology. Part IV.considers theaggregation problem and related statistical issues in greater detail,

II

EDUCATIONAL THEORY AND EMPIRICAL PRODUCTIONFUNCTION ESTIMATION FOR EDUCATION

The purposes of this Part are to indicate the requirements for causally interpretable, non-experimental researah into educational technology, and to provide some initial suggestions regardingthe appropriate strategy for such research. First, the relationship of theory to empirical research isconsidered; it is stressed that non-experimental or observational research requires a theoretical frame-work with which to identify important variables and to specify the algebraic form of the relationships.Second, the theoretical literature of education is examined in an attempt to develop a tentative model ofthe educational production process. The discussion is organised into investigations of the inter-temporalstructure of education, the theory of classroom learning and the theory of educational administration.The recursive structure of student development is supported both with speculative analyses and empiricelstudies. The consideration of classroom learning departs from soveral earlier studies in that it is notexplicitly concerned with abstract learning theory but rather focuses upon instruction. The discussionof administrative theory is designed to illuminate educational decision-making, particularly with respectto the extent to which educational developments aee innovated.

The Role of Theory ia Empirical Research

The dangers of adopting a strictly empiricist research strategy have been widely discussed in theliterature of sociometric and econometric researcht. The discovery of a systematic relationship be-tween two variables suggests several hypotheses. The two variables may be causally related, althoughit is uncertain in which direction the causation might operate, or, indeed, if a unique direction of cau-sation may be identified; examples of mutual causation abound in the study of social systems. Alter-natively, the two variables may share a common source of causation or may simply measure the samelatent concept. In the absence of a theory of the process to guide in the specification of functions to beestimated, the results of statistical analyses may only be regarded as predictive as opposed to causallyinterpretable. The empiricist study describes phenomena in terms of measurable variables and mayenable one to predict a more elusive variable through the use of readily available measures; such astudy does not, however, provide an empirical basis for conclusions regarding the consequences ofmanipulating particular variables. The policy oriented study of educational technology being consideredhere requires that the results of the research be causally interpretable and that one be able to evaluatethe consequences of manipulations of school input variables.

The statistical technique of multiple regression analysis produces estimates of the parameters ofa linear function such that the estimated values of the dependent variable are as highly correlated aspossible with observed values of the dependent variable. The technique by itself does not generate or

1. One of the best stateMents regarding the potential dangers of the strictly empiricist approach it found in Tialling1, Koopmans, "Measurement Without Theory", Review of Sconomics and Statistics, August 1041, pp, 161.112,

47 13

test causal hypotheses, nor does it provide a rigorous basis for selecting variables for analysis orfunctional relationships. A number of scholars have demonstrated that the selection of variables andspecification of appropriate functional forms must be based upon a priori, and deductive theoreticalanalyses of the process under study. Regression analysis may then be appropriately used to estimatethe strength or magnitude of the association of variables,

Successful generalization of the production function concept to the study of educational technologythus requires that an adequate theory of the educational process be obtained. Most empirical researchinto educational technology has simply identified the variables which casual empiricism would suggestare relevant and proceeded to assume that the computationally-expedient, linear form is appropriate.The idea that educational achievement is simply the sum of the independent influences of a number ofschool inputs is intuitively absurd. Recently, it has been suggested that the field of learning theorymight provide insights into the appropriate specification of educational production functions.

Educational Theory and the Modellinj of the Educational Process

This section offers an approach to the specification of educational theory that would furnish thenecessary basis for production function estimation. A review of theoretical discussion and empirioalresearch relating to educational processes suggests variables whioh are appropriate to a quantifiablemodel of the educational process. A detailed model of the educational process would be both beyond thescope of the present paper and premature, given existing knowledge; the section is thus meant to besugges''ve only.

This discussion differs markedly from earlier efforts in that it considers educational processesfrom the viewpoint of the literature of educational theory and research. Previous efforts at constructingquantifiable models of education have been characterized by their conspicuous lack of a basis drawn fromeducational literature. Intuitive Justification for a model composed on the basis of empirical expediencyhas been offered by reference to a small number of empirical studies and theoretical summaries. Whilesuch efforts are notable in their intent, approaching the problem of estimating quantitative relationshipsin education without an understanding of educational processes increases the danger of misspecificationof underlying principles and consequent misinterpretation of empirical results.

This discussion will be divided into two subsections. First, the general structure of the educationalprocess will be studied to illuminate the issue of an appropriate choice of model structure. Second, thetheory of education and of the administration of education will be perused to obtain insights into theclasses of variables which affect the educational process. Following this section, the measurementand conceptualization of variables will be discussed to suggest approaches to securing data and facili-tating the estimation of model parameters.

a) Structure of the Educational Process

Education is a sequential process in which a learner's prior knowledge is affected (increased,altered, or eliminated) by new experiences. The outputs from one stage of the process serve as inputsto another. Thus, education may be viewed in a recursive framework which represents a dynamicprocess as a series of sequential stages, each one dependent upon past stagest, This approach inci-dentally coincides with the design of formal educational structures which employ grades, levels or typesof schooling.

The view of education as a recursive system is consistent with existing knowledge of intellectualdevelopment, the learning process and the institutional structure within which education takes place.At the most naive level, it is apparent that mastery of prerequisite, basic skills is crucial to future

1, H2O,A, Weld, "A Generalization of Causal Chain Models", Econometrielii 28, Zi April 1060, pp, 448483,

48

academic success: basio verbal, reading and arithmetic skills are necessary inputs into more advancedliterary or quantitative subjects. Less obvious is the exact nature of the role of prerequisite knowledgein intellectual development. Work by the pioneering psychologist, Jean Piaget, indicates that individualsmust pass through three stages of intellectual development with respect to any subjeotl, First, one ac-cumulates concrete knowledge about the subject; second, one develops generalizations based upon con-crete experiences or knowledge; finally, one resorts to abstraot analysis of the important aspects ofevents or phenomena. Abstractions are meaningless in the absence of general and concrete referents,

The importance of prerequisite knowledge to student learning has been amply supported by empiricalresearch. Research studies indicate that a student is not able to perform a "higher level" learning taskif he has not been able to perform a "lower level", or prerequisite tasks Where prerequisite taskswere taught and mastered at some level, the success rate at learning new tasks far exceeded that ratewhich is normally observed in educational practice. The widespread research procedure of statisticallycontrolling for previously measured abilities in studying effects of curriculum materials or instructionaltechniques demonstrates implicit recognition of the role of prior knowledge as an input in the eduoatienalprocess.

Grade levels, cycles or forms characterize the institutional structure of educational systems inmany countries, While orginally an expedient resulting from the need to meet the demands of wide-spread education with limited resourees3 , the stroture has continued because of its Convenience aswell as its economic rationality. Many recent attempti at individualized instruotion4 , and non-gradedschools" , reveal a trend which may eventually replace the rigid institutional patterns of the past. Whilethis trend will have long-range implications for research into educational processes, some of the prac-tical, logistical problems posed by attempts at genuinely individualized instruction indicate that in thenear future educational researchers will for the most part be working with data generated from gradedschools,

A recursive model of eduoation has the praotioal advantage of permitting one to examine the effi-ciency of school resouroes committed to various levels and subject areas of the educational programme.Empirical analysis might, for example, indicate that development of reading skills should be givengreater emphasis at the expense of arithmetic skills in early grades. Furthermore, a recursive modelpermits one to examine the performance consequences of inferior educational experiences at eaoh gradelevel, The appropriate level of disaggregation over time and subject matter is oonsidered below in thediscussion of conceptualization and measurement of variables, and again in the review of statisticalestimation prooedures,

b) Theory of the Educational Process

Educational theory provides insights into the ideatifioation and delineation of facto.os affecting edu-cational achievement, An attempt to determine the appropriate variabies and the nature of their influencesuggests that two types of theories :must be examined - eduoational theory and administrative theory,Educational theory describes the nature of the educational process and the manner in which learningoccurs, Administrative theory indicates the way in which decision-making affecting the allocation of

1, John H, Flavell, The Develo mental sylp.212gyjapaPiaget, Princeton, New Jersey, D. Van Nostrand Company, Inc, ,

2, Robert Gagne, "The Acquisition of Knowledge", bysimIggiagaitsky, 69, 1062, pp, 366.366$ and Gagne, 1,R. Mayor,1.1, L, Garstens and N.B. Paradise, "Factors in Acquiring Knowledge of a Mathematical Task", Esyclologicai Monompla 16, 19621Vol. 1, Whole No, KJ,

3, R, L, Butts and L.A. Crernin iliaggy of Eduoation ip American Cultpre, New York, Henry Holt, 1989,4, "Association for Supervision and ClifficUltim Development, "1ndividueiit1ng In truotioq, 'Washington! the Auodiation, 1964,

and "National Society for the Study of Education", Lusilajagigg Instvuotioqi Chicago! University of Chicago Pram 1082,8, John Goodlad and Robert H, Anderson, Ijksjimgraded Elementary...WEI, NeW Yorks Harcourt, Brace and World, 1960

1963,

40

is

resources to and within education is conducted, Thus, one provides the technical basis for the produ i-tion function and one describes the "market" within which education occurs, The following discussionwill treat first educational theory and then administrative theory.

i) Educational theory

Variables influencing the educational process may be considered within three Oases, Exogenousvariables are defined as those external to the educational system and hence beyond the direct controlof educational decision makers. Endogenous variables are those input variables which may be manipu-lated by the educator and which are aspects of the educational process, The third class of variablesincludes educational outputs. This conceptualization of "fduclation variables is somewhat artificial inview of the dynamic nature of education; exogenous inputs into schools are augmented and transformedinto school outputs which are later useful as endogenous inputs. Nonetheless, this classification ofvariables clarifies our discussion of educational theory.

The relationship among these three classes of variables may be summarized as:

Et = P (E X,

N )

where Et = output for some measurable aspect of school effect for period t;

Xt = input factors exogenous to the formal educational system;

Nt = input factors endogenous to the educational system.

Each of these three classesas:

Variables within E:

is, in turn, made up of several sets of variables, which may be identified

C = cognitive skills,

R = affective responses,

D = physical development.

Variables within X1 A = aptitude: genetic endowment supplemented by experience,

P = prerequisite knowledge: verbal, analytic and substantive skillsnecessary for academic success,

M = motivation: activity directed or sustained towards a scholarly goal.

Variables within N: S = schooling process: curriculum, instructional method, teacherexpertise,

L = classroom: teacher interaction with students, peer culture,

F school environment: facilities,

The following discussion will suggest a theoretical basis for the inclusion of each set of variablesin a model of the educational process and will provide a summary discussion of related research findings,Space does not permit an exhaustive review of educational research, nor the synthesis of the factorsidentified here into an elaborate model. The purpose of this discussion is to illuminate, for personsoutside of the professional sphere of the educationist, critical factors which should be considered by allscholars attempting research into the effects of education,

The present discussion differs from previous approaches to the identification of variables significantin studying education in at least one major aspect: socio-economic and cultural variables are not in-cluded in the discussion peraip.: In excluding them, the author is not ignoring the significant correlative

50

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findings linkirg educational achievement with class or soelo-eoonomic status, Many factors influencingeducational ou0omes which may reflect oultural characteristics are noted in the following discussion,However, attempts have been made to keep the variables identified here as abstract as possible. Theuse of socio-eeonomie characteristics as proxy variables for more basic traits important to educ'ationis highly subject to criticism and will be explored in detail below,

The important issue of obtaining suitable measures of variables arises for almost every variable treatedhere. Therefore, related questions and their implieations will be examined in the next part of the paper,Specific measurement problems will be mentioned only if they illuminate an important aspect of the useof the variable in empirical research,

Educational output (E)

An extensive literature on the goals of education suggests the heterogeneity of output which is fre-qttently desired as the result of schooling1. Of the three domains2 of educational output wh:10% are pre-sented here (cognitive skills (0), affective responses (R), physical development (D)), the developmentof the first two is most likely to be dominated by the schools and, hence, they will constitute the formaloutput of schools for purposes of the present discussion.

The two areas of cognitive skills and affective responses have been treated separately in taxonomieswhich list educational objectives according to hierarchies of skill and abstraction required for their mas-tery. Yet, in the recursive educational process, the achievement of an objective in one domain may actas a prerequisite or motivating faetur for subsequent achievement and, hence, distinctions between thetwo domains are not always evident. No attempt has been made to separate the domains into disjointcategories in the following discussion of educational inputs, Specific input factors are examined as theycontribute to output identified with one or the other or both domains.

Educational inputs: exogenous factors (X)

While student characteristics, the exogenous factors, maybe regarded as the raw inputs into theeducational production process, because of the recursive structure of schooling, these variables arepurely exogenous factors only in the initial period. After having been operated upon by the educationalprocess, the analytic distinction between exogenous and endogenous becomes somewhat blurred. In thefollowing discussion, exogenous factors are presented in such a way as to suggest the impact that school-ing may have upon them,

Aptitude (A)

It is easy to verify that individuals of the same age rarely at any given time are able to performexactly the same sets of tasks, This characteristic, commonly called intelligence or aptitude (the twoterms are used interohangeably here), affects seholastio performance, This attribute is not constantfrom birth° but, rather, represents a developmental characteristic4, The intelligence quotient

1. For example, see Rockefeller Brothers Fund, "The Pursuit of Excellences Education and the Future of America", panel Re-paadjiejp_esaatsittei.pgjgg, Garden City, New York, Doubleday, 1nc1 10681 L W, Gardner, "National Goals in Education",

the s t e Re of e .reside t o Ago o, _ Englewood Cliffs, New Jerseys Prentice-Hall, 1960:

and C, M, Lindvall (EC), Defining Educational Objectives, Pittsburgh, University of Pittsburgh Press, 1964,

2, From B,S, Bloom, 6,:msamy.9attatia_ia saiatim, Ws:slave Domair, New Yorks David McKay, Inc, , 10651 andDavid Krathwohl, itaunalny,Ifiltapaatil.gbiggati Affeotiva Domain, New Yorks David McKay, Inc 1904,

3, J,P, Guilford presents evidence refuting this widely-held principle in The Nature of Hutnanintelligerice, New YorksMcGraw-Hill Book Company, 1067, See also j.M, Hunt, Imalgence and Expaigni New Yorks Ronald Press, 1961,

4 B, S, Bloom, ,StabililyjaSte e in Human Cnariloteriitioio NeW York, John Wiley and Sone, Inca1 1964.

(IQ) compares actual achievement of an individual at a given age with that of a normeci population. Themeasure includes the influence of environment on a person's knowledge at any point in time, Thus,when used as an empirioal variable in research, intelligenee is an intermediate concept incorporatingprinciples of genetic endowment and environmental influence in the form of past experience.

In addition to showing that intelligence as measured by IQ is a variable factorl , research alsosuggests that the influence of environment upon intelligence is greatest in the early years of a child'sdevelopment, Particularly, lack of learning in one period is difficult, sometimes impossible, to makeup in later periods5. Measured differences in intelligence which previously were attributed to ethnio orclass intelligence differences may reflect this modifying influence of environment3.

Prerequisite knowledge (P)

Prerequisite knowledge may be considered as a specific extension of the environmental componentof aptitude. It encompasses academic abilities exclusive of social and environmental factors. Theimportance of prerequisite knowledge to student achievement in learning tasks has already been men-tioned to lend support to the consideration of education as a recursive process4.

The role of prerequisite learning in various disciplines can be expected to vary significantly, de-pending on the technical nature of the material being studied andtheneedfor highly specific principlesor tasks as prerequisites. This, in turn, would suggest that an educational production function shouldbe disaggregated by subject, as the role of prerequisites in one subjeet (e.g. mathematics) may beconsiderably different from that in another (e, g, fine arts or literature). In instances where earlyprerequisite knowledge was missing, and where it was highly important, the academic advancement ofa student would be expected to decrease rapidly and approach zero, unless tho academic situation wereone which would allow instruction at the level of the student's need. In short, the problems of poorachievement may be expected to compound, suggesting that the relationship between adequate prereq-uisites and armlemic success is non-linear.

Motivation (M)

The definition of motivation as "the combination of forces which initiate, direct or sustain activitytowards a scholarly goale ", implies that motivation is a composite of qualities including expectation andreinter( 9ment. While theoretical discussions of motivation are ambiguous, or even contradictory, it isapparent that some minimal amount of motivation must be present before learning can take placee.Beyond that, theoretical works are in conflict, lt has been asserted that performance increases monot-onically as motivation increases implying that the most effective instruction occurs when motivationis maximal. A more plausible argument is that before motivation can faellitate performance, correct

1. Extensive evidence to support this conclusion is provided in Robert L. Green and others, INLAWILtigialitittAnsof Chilo oo s, Washington, D. t Department of Health, Education and Welfare, United States Office of Edu-

cation, Cooperative Research Project No, 2321, 19641 Otto Klienberg, aninallownsUgleittutafiggp, New YorksColumbia University Press, 19351 E. S. Lee, "Negro Intelligence and Selective Migrations a Philadelphia Test of the KlienbergHypothesis", Americap ,S,od_ologisALLyja:4e , XVI, 1951, pp. 227-233,

2. 13,8. Bloom, itallyAuLftbagg jiumniushawsu_Los, New Yorks John Wiley and Sons, Inc., 1964,3, Martin Deutsch and Best Brown, "Social Influences in Negro-White Intelligence Differences", journal of Sociillssues,

April 1964, pp, 24-35.4, Robert Gagne, "The Acquisition of Knowledge", gpA_sa,6, William W, Farquhar, "Academic Motivation and Inner-City Schools", in Herbert C. Rudman (Ed, ), Urban Schooling,

New Yorks Harcourt, Brace and World, Inc., 1068, p. 198,6, John W. Atkinson, Anintroduction to Motivatioll, Princeton, New Jerseys Van Nostrand, 1954,1. C. E. Osgood, etIL..no Ala erimental Psylbasy, New Yorks Oxford University Press, 1953, p, 413,

52

or otherwise desired behaviour must be dominant over other possible behaviour patterns' , In otherwords, motivation can be disfundional with respect to academie achievement if habits which facilitatelearning do not exist, Research results on the effocts of motivation upon academie achievement alsosuggest that achievement motivation in a given situation is dependent on both the individual's typicallevel of motivation and the degree to which he sees the situation as achievement relevant2 , Thus, astudent must be able to see the relationship of a particular task to an achievement goal,

enclogets factors N)

Endogenous factors are those over which educational policy makers have the most immediate control,namely, school characteristics, Studies of the influence of these characteristics on educational produc-tion have special significance for the issues of allocation of resources to and within the educational sys-tem,

Schooling process (5)

Curriculum quality, instructional method and teacher. skill are important in educational production,Schooling process variables which deal with these aspects of educational practice measure the efficiencyof the educational system, Educational research is abundant in these three areas. No doubt part of theinterest in research of this nature has been stimulated by the widespread educational reform which hasoccurred in the past decade in many subject areas in a great number of countries. The three classes ofschooling process variables cited here - curriculum organisation, instructional method and teacher skill -will be discussed separately,

The majority of research studies in curriculum have utilized formal research designs to study aparticular problem at a micro level, Results from these studies suggest that student achievement isrelated to curriculum objectives, As an example, many experiments have tested the efficiency of "new"versus "old" mathematics curriculum materials. In instances where subjects are tested with instrq-ments designed on the basis of each set of materials, subjects using traditional materials typicallyperform best on tests designed for traditional programmes stressing mechanical skill in problem solv-ing, and subjects using new materials perform best on new tests designed to measure analytic abilities°.These results imply that a critical aspect of the study of educational production functions is the choiceof an objective function made with reference to the cultural, political, social and economic needs of thestudents in a particular educational system.

Research in instructional methods has illuminated psychological principles of learning efficiencyand the influence of ability factors on learning patterns. It is not the purpose of the present summaryto present in detail the research findings which have contributed to an understanding of student learning,However, some results have implications for the structuring of educational production research studiesand will be summarized here.

Numerous studies suggest interactions of ability and the effect of knowledge of results upon achieve-ment, If students' knowledge of the success of their academic performance is immediate, there appearsto be no correlation between ability as measured by IQ and performance, or between reading level andperformance4. When knowledge of results is less immediate, both IQ and reading level correlate with

1, W, Spence, labalosapary.aajcadj=ng, New Havem Yale University Press, 1066,2, Elizabeth 0, French, "The Development of a Measure of Complex Motivation", United States Personnel Taikingpseatch

gssitallgataaepat, No, 56-68, 19581 and French and I, Chadwick, "Some Characteristics of Affiliation Motivation", journal2fArainausoghyslagiy, No, 82, 1058, pp, 2964305,

3, Milton Maier, "Evaluation of a New Mathematics Curriculum", American Psygbalgga No, 11, 1962, p, 338,4, L,D, Eigen, "A Comparison of Three Modes of Presenting a Progammed Instruction Sequence", jourpal of Educational Re-

Nc, 65, 1962, pp, 453.4801 and i,K. Little, "Results of Use of Machines for Testing and for Drill Upon Learning in Educa-tional Psychology", 12gvalsilepla No, 3, 1934, pp, 45-40,

53

perfornanco on immediate and delayed post-tests. In addition to suggesting that the use of reinforce-ment through immediate feedback can be expected to have greater effect on poor students than on supe-rior ones, these results suggest that the impact of instructional method on students of different abilitiesshould not be uniform,

The growing use of a variety of media for instructional purposes has raised many questions regardingboth the pedagogical effectiveness and the economic efficiency of mediated instruction, Abundant researchin the field of instructional media has been carefully summarized'. Research indicates sssentiallythat teachers and media can both be used for effective instruction, When extraneous factors are removedfrom an experiment in instructional effectiveness, significant differences almost never appeara At thesame time, when a comparison of methods focuses on a task for which a teacher is well-suited, class-room technique appears more effective, When a comparison considers a subject which requires particu-larly detailed, mediated presentation, the media is likely to appear most effective0, These results in-dicate that the educational policy maker has available numerous means of meeting particular goals.They also suggest that economic criteria may well be highly relevant at a time when resources for edu-cation are at a premium, Unfortunately, almost no research has examined the issue of expenditure al-location within schools to achieve optimal results from staffing patterns, technology and other facilities4,

Teacher skill influences educational outcomes, Teachers have considerable influence over whattranspires in the learning process as they manipulate aspects of the instructional situation: a teachermay control the stimulus situation, the verbal communication used to direct the learner and the positiveor negative feedback to the students from the events of instruction6. The feedback to students acts aspositive and negative reinforcement and affects academic performance directly by guiding students'progress and indirectly by affecting motivation levels°,

Theoretical studies and empirical research on teaching methods to facilitate learning have relatedteacher effectiveness to learning principles. However, in spite of theoretical constructs outlining thenature of teacher effectiveness, research attempting to measure teacher effectiveness has producedlittle concrete evidence regarding the factors which are responsible for teacher quality" Furthermore,no fully satisfactory measures for teacher quality have been found, Commonl! used variables such asteacher verbal aptitude, experience and academic background do not provide consistent resultse. Thesevariables probably act as proxies for more basic and relevant variables which remain elusive,

1, Pot comprehensive bibliographies see, W, Schramm, "Learning from Instructional Television", ag o Ecmd_t._Igg,U2Ig.IA-IpALch, No, 32-2, April 1982, pp, 166-1611 Robert Glaser (Ed, ), Teatisg act&alatilg,d Pro atg ecr.....EU.g, Washington, D. C, $National Education Association, 1966$ M, A, May and A.A Lunsdaine, "Mass Communication and Educational Media", Annual Reviewof Psy/ (hAgy, 1966, pp, 416-6341 and B, C, Duke (Ed.), Survey of Educational Media Researphin_the Far East, Washington, D,C, ,

United States Office of Education, 196362, D, W, stickels, kCtittca1 Review of the Methodology aud Results of Research Comparing Television andlok-to-Fac,e Ins-

truction, unpublished doctoral dissertation, Pennsylvania State University, 1988,3, Wilbur Schramm, Philip H. Coombs, et al The Key Medial Mem to Educatioal Plannero, Unesco International Ins-

titute for Educational Planning, 1961,4, Bruce R. Joyce, "Staff Utilization", ReNiew of Educational Research, Vol, XXXVII, No, 3, June 196/, pp. 323436,5, Robert M, Gagne, 'I' e Cot.b_giaguas1 tuigg, New Yorkt Holt, Rinehart and Winston, Inc, , 1986,6, E,B, Page, "Teacher Comments and Student Performance", Journal of Educationallanbo12gy, Vol. XLIX, 1968, pp, 1/3-

1811 and Pauline S. Sears and Ernest R, Hilgard, "The Teacher's Role in the Motivation of the Learner", in Zesikata_rInstmtion, 63rd yearbook, National Society for the Study of Education, Chicagot the Society, 194, pp, 182-209,

Pi, For example, see A. S. Barr, LW, "Wisconsin Studies of the Measurement and Prediction of Teacher Effectiveness I ASummary of Investigations", lomat of Experimental Education, 1961, pp, 1-155,

8, One of the more extensive studies is that by David G, Ryans, chsluelmatlattaLlatzegjpagnavipagnjaippagl, Washington, D,C, t American Council on Education, 1080, Other studies, including that by J, A, Shea, reveal verylow correlations between measures of teacher effectiveness and mental ability, ("The Predictive Wee of Various Combinations ofStandardized Tests and Sub-teats for Prognosis of Teaching Efficiency", Catholic University of America, kcit_Lcbional Research,lioLagro apla 19, 1965, No, 6),

84

2'0

Classroom factors (L)

Learning is not exclusively influenced by cognitive considerations, Teacher personality and peergroup attitudes affect motivation, and henap aehievernent, while a student is in an academic situation,These significant classroom facthils operatelaultaneously with the learning process,

Several aspects of teacher personality have an impact on classroom climate, The extent to whichthe teacher offers an image which the students regard as an "ideal" may affect their willingness to per-form academic tasks, This may in part explain the difficulties typically encountered by middle-classteachers reared in suburban areas when they attempt to teach ghetto children1, In addition to the effectsof different cultural environments of students and teachers on academic achievement, the interaction ofteacher personality and student personality factors frequently acts to encourage or inhibit academicprogress,

Research on the effect of teacher behaviour over the cycle of learning units and sub-units hasprovided insights into the effect of teacher behaviour upon student achievenient,

There is a direct relationship between a teacher influence which encourages student participationand constructive pupil attitudes towards the teacher3 Research specifically studying the relationshipbetween teacher influence and student achievement suggests that attitudes and achievement of studentsare superior when classroom teachers are able voluntarily to vary their influence upon the class duringthe learning cycle and are able to diagnose student needs and respond with appropriate actions 3

Research results also indicate that the effect of teacher influence varies over a learning cycle andthat the most effective known patterns of teacher influence, from the standpoint of student achievement,consist of varying levels of indirect and direct influence on student actions, Thus, highly disaggregatedstudies which examine the nature of teacher influence over short periods of time should be the mostuseful in constructing production functions designed to reveal optimal patterns of teacher behaviour4Indirect teacher influence appears to be positively correlated with student attitudes, therefore differingforms of an educational production function could be expected from different objective functions,

The adolescent sub-culture has been shown to be generally detrimental to academic motivation andachievement5. A strong correlation between social rewards for academic excellence and the ability ofhigh performers among high school students, regardless of other school characteristics - such as size,community, socio-economic status, expenditure per pupil - suggests that the most capable students willbe high achievers only if it is socially acceptable. A significant influence upon boys' choice of an "ideal"image appears to be interscholastic athletics, perhaps because of the importance attached to these activ-ities at a school and community level, In schools which do not have interscholastic programmes, theideal image is more academic than in comparable schools with interscholastic athletics. For girls, thebasis of the status system is more inclined to wander, though in all cases it also tends away from aca-demic excellence,

1, Daniel Schrieber, "The Role of Univetsities in Supplying Help to Metropolitan School Systems", in Herbert C, Rudman andRichard L. Featherstone (Eds, ), .12haLSibitgliog, New York: Harcourt, Brace and World, 1988, pp, 33-61,

2, Ned A, Flanders, "Teacher Influence, Pupil Attitudes and Achievements: Studies in Interaction Analysis", Final RepoutoQuerative Research Project No, 30/, Minneapolis: University of Minnesota, 1960,

3, Ned A, Flanders, "Some Relationships Among Teacher Influence, Pupil Attitudes and Achievement", in Bruce J, Biddle(Ed, ), Contemporary Research on Teacher/ffectiveness, New York: Holt, Rinehart and Winston, 1984, pp, 198-231,

4, David 0, Ryans has shown that pupil behaviour is more closely related-to teacher behaviour in elementary grades than insecondary grades, in Charactetistics of_Teachersk Theitnesctiption. Comparison and_Applaggi,

6, James 5, Coleman, "Adolescent Sub-culture and Academic Achievement", TheAmericarilouthatuf Sociology, No, 66,January 1960, pp, 331-34/,

55

21

Poor school environment (F) hap also been shown to have a detrimental effect on measured studentaptitude' , These results appear to contradict the findings of major empirical school oharacteristicsstudies which allege that school inputs have negligible effects on student performance,

11) Administrative theory

Knowledge of administrative theory is less complete than is knowledge of the educational process.Furthormw:e, progress in forming a theory which is sufficiently well specified to be subjeeted to em-pirical ertimation may be slow9 However, some surveys of the literature have been made which permitobservations on the direction which research relating to aspects of administrative behaviour is currentlyassuming°.

Studies of administrative behaviour in schools, most of which are doctoral dissertations, havefocused upon the social setting from which decisions emerge. For example, studies have investigatedthe leadership role of pr'-cipals and administrators in both the educational system am' in the community4or surveyed the perceptions of teachers regarding the roles of principals and superintendents". Fewstudies consider the formalization of the decision process ; nowhere does research attempt to identifythe criteria on which policy decisions are made or the rationality and effectiveness with whioh thesevalues might be pursued, One hypothesis which has considerable intuitive appeal is that decisions byschool administrators are made primarily to preserve a community consensus and support staff morale.Because of the essentially conservative structure of educational systems, there is no a priori reasonfor expecting decisions affecting resource allocation in schools to be made with an efficiency criterion,

An understanding of the nature of ant4 bases for administrative decisions remains a challengingproblem in attempting the estimation of empirical produotien functions for education?, ff the observeduses of resources in schools are to be interpreted as effioient in the sense that no greater level ofstudent achievement could be obtained from the resources, then one must be able to presume that de-cision makers are aware of what constitutes best practices and, in addition, strive to adopt these pol-icies,

1, Kenneth B. Clark, D_ark Ghetto, New York: Harper and Row, 19661 Ada Hart Ar1itt, "The Relation of Intelligence to Agein New Children", The dcurnal of Applied PsyslAsy, VI, 1922, pp, 378-384; Helen Tomlinson, "Differences between Pre-SchoolNegro Children and Their Older Siblings on the Stacforcl Wet Scale0, ,lournal of Nem Education, XII, 1944, pp, 474-479; andFlorence M, Young and Howard A, Bright, "Results of Testing 81 Negro Rural juveniles with the Wechsler intelligenceScale for Chil-dren", 12g,n,a1 otsocial Psylkstegy, XXXIX, 1954, pp, 219.226,

2, Daniel E, Griffiths, "Toward a Theory of Administrative Behavior", ildasissigyipal_y_taior Edueation, Ronald F, Campbelland Russell T, Gregg, (Eds,), New York Harper and Brothers, 1967, pp, 365-366,

3, Keith Guy Hogle, ResearoltRegigto/kkatattukbay, unpublished :.laster's paper, University of Whconsin, 1966,4, Martin Gra ,, Rci...40AL,IalyikiLtbaskoLt ttigLip lilljp, unpublished doctoral thesis, University of Wisconsin, 1961,6, Arthur Blumberg and Edmund Amidon, "Teacher Perceptions of Supervisor-Teacher Interaction", Mministraviv4. Igo**,

14-1, September 1066; John Herbert Crotts, A Coituvitajatiagidulthiugastensuagut the mapagyislatasuipilunpublhhed doctoral thesis, University of Missouri, 19C31 and William Emil Ktischman, Lapjy of Pdnoioal-TeaohqBehavioral

Adminitai4eirslos, unpublhhed docto:al thesis, Indiana University, 1964,6, Two studie$ tich do teat decision-making are Arnold Roe, Anitip e i c Utiatu 0 0 . un-

published doctoral thes% University of California, Los Ange104, 10641 and Walter John Ziegler, limagiund P oca_r_jaiskjilmos

alU jingly_tthpainipattufjakcals, unpublished doctoral thesis, University of Southern California, 1964,7, The need: for the development of theory and ita application to administrative research in all fields was noted by Herbert A,

Simon in ii,dministrativis Behavior, New Yorki The MacMillan Company, 1968, 15, 44,

A6res,oKawo

SUMMARY

This part of the paps:: has surveyed the role of theory in empirical research into educational prac-tices, In addition to underscoring the need for a theoretical framework for school characteristics studies,it has drawn upon the literature of educational theory and research to suggest a tentative model of theeducational prooess. The absence of a comprehensive administrative theory has been noted as a majordeficiency whioh must be corrected in =ler to supply meaningful interpretations for inter-school studies,

2347,

f,1

III

MEASUREMENT AND CONCEPTUALIZATION OF VARIABLESFOR PRODUCTION FUNCTION ESTIMATION

This part surveys the major problems that emerge in any attempt to conceptualize or measure thevariables entering the educational production function, These problems occur in connection with fourtopios; a) the use of proxy variables to represent underlying and ill-defined variables; h) the scalingof qualitative and nominal variables; c) the reliability of observational instruments and the implicationsof the inter-,correlations of variables for the interpretation of regression results; d) the selection ofan appropriate level of aggregation both over subject areas of instruction and over grade levels,

The Use of Proxy Variables

The principal reason for the use of proxy variables in quantitative research into educational pro-cesses is the lack of a well-developed theory of the educational process. The abstractions of the edu-cational process which are currently accepted contain variables which do not have empirically conve-nient counterparts, The researcher is therefore forced to resort to a variety of derived measures ofthe underlying concepts. Motivation and teacher quality are examples of educational system inputs forwhich only crude or extremely time-oonsuming measurement techniques exist . Researchers havetherefore resorted to indicant or proxy variables which appear intuitively to be highly correlated withthe underlying variables, Motivation and pre-school learning have been measured by the proxy variablesocio-economic class of the student's family2, In studies of educational production, the age of theprircipal structure of the school has been employed as a measure of the quality of the physical plant andof the technological vintage of school facilities°.

The use of'proxy variables introduces critical problems into both the quantitative analysis andthe interpretation of results, The variable socio-economic class of family, for instance, allegedly re-presents the variables motivation and, in some studies, pre-school achievement, However, somesociological studies indicate that socio-economic variables have little predictive power when morebasic student or school characteristics are considered4, It is therefore questionable whether the vari-ation in some dependent measure attributable to socio-economic class of family is properly regardedas the result of the latent variable motivation or some unknown combination of the other variables whichmay be correlated with family social class,

1, one interesting but difficult Mande of motivation is that of proiective or thematic apperception tests developed by DavidC, McClelland and his associates, described in The Achievement Motive, Princeton, New jersey: Van Nostrand, 1961,

2, jessenurkhead, lzpiluligOutput in Large.C1101:41-Schools, Syracuse: Syracuse University Press, 196'7, p, 43,2. Ibid., p. 44,4, Patricia C, Sexton, Ed oatiokand Income, lmialitie_thois, New York, Viking Press, 19611 James S.

Coleman, 'Pe Adolescent Societyl The Sooiq Lye of the andits_lmaoton New Yorbi Free Press of Glencoe,196i1 David Gottlieb, "Social Class, Achievement and the College.Ooing Experience", plool Review, 70, Autumn 1962, pp. 273.2861 and Wilbur B, Brookover, Ann Peterson and Sheller Thomas, Self Conceplajtalituadieve ent, East Lansing,Office of Research and Publications, College of Education, Michigan State University, 1962,

59

24

Proxy variables also confuse the interpretation of research results by obscuring the identity oflatent variables, The easily accessible variable soolo-econornio olass of students may measure moti-vation or pre-school education, as several authors have suggested; however, equally.compelling argu-ments may be offered that socio-economio class is really a more refined and precise measure of thequality of school inputs; in studies where the decade of construction of the principal structure or thepresence of science laboratories have been used to measure the quality of inputs, this argument isparticularly convincing. Broad, proxy variables introduce ambiguities into research into educationalproduction functions which are impossible to disentangle.

The Sealing of Qualitative and Nominal Variables

The objective of production function analysis is to determine the responsiveness of outputs to se-lected, controllable inputs; this requires that metric significance be attached to both independent anddapetrient variables. Economists have adopted the convenient device of resorting to money valued vari-ables to free themselves from the task of examining the metric significanc$ of empirical measures.The abundance of both qualitative and nominal variables in the discussion of the eduoational processforces one explicitly to consider questions of the unit of measurement and the point of origin of mea-sured variables.

The problem of scaling appears in educational production function estimation in the analysis ofqualitative and nominal variables, Most of the indicants of quality of school inputs and of school outputsused in studies to date are qualitative in nature, Class rank, level of motivation or ability are examplesof non-metric qualitative data which are of ordinal significance only. Class rank, for instance, whileproviding an ordering of students, does not indicate the distance between observations: moving from2nd to 1st in a class probably requires substantially different accomplishments and efforts than movingfrom 543rd to 542nd, Similarly, teachers with verbal ability measures of 140 cannot be assumed to bein some sense 40% better than those with verbal ability measures of 100, Clearly, the metric signif-icance which can be conveniently attributed to economic variables by means of market evaluation cannotbe assigned to these qualitative variables,

Nominal variables are those variables to which names have been assigned without regard for somelatent dimension, Geographic region or race are examples of variables which might be assigned toarbitrary numerical categories. A less obvious example is socio-economic category based upon theprofession of the father. In studies of educational production where socio-economic class is assertedto be an adequate derived measure of motivation and informal education, these nominal variables havebeen introduced into the regression analysis as though they were well-scaled variables, The changesin class, as persons move from categories of servant to unskilled, and managerial to professional,have been assumed in quantitative analyses to be in some respect the same,

An extensive literature on the theory of scaling exists in psychometricsl. While no attempt willbe made to summarize techniques incorporating this theory here, some general comments should bemade. The purpose of scaling theory is to provide an intuitively satisfying model of origin and intervalwhich will adequately capture the significant dimensions of variables, Scaling is, of course, importantin interpreting ordinal data; the problem of socio-economic class might, for instance, be reduced ifappropriate orderings of latent variables were merged into a multi-dimensional metric which provideda semi-cardinal representation of the variable, A usefu; set of qualitative variables might be obtainedfor class which indicates the approximate distance betwecn occupational or income groups in terms ofthese latent characteristics, Socio-economic class could, in such an instance, be used as an indicantfor a set of underlying concepts which are rather difficult to capture or measure.

1, See, for example, W,s, Torgerson, =go and Methods of Nils New Yorki John Wiley and Sons, 19581 P. C..00mbs,

"Psychological Scaling without a unit of Measurement", Ps cholo ioal Review, No, 8'l, 1980, pp. 148-1881 and Robert P, Abelsonand John W, Tukey, "efficient Conversion of Non-Metrio In ormation into Metric Information", PrO eediAgi of the American StatisticalAlitc=Uitgaggs, 1950, pp, 228430,

The Reliability of Observational Instruments

Standardized examinations for ability and achievement exhibit somewhat flexible standards of mea-surement. Any examining instrument, in addition to measuring the latent charaoteristio, also measuresthe influence of a variety of immediate factors, from the health of a subjeot on a partioular clay to thecomfortableness of the testing room. Reliability ooeffioients reported for standardized academic) testsrange from approximately .85 to .081, Yet, rarely aro these figures quoted for sub-populations, Thus,tests may be leas reliable for unusually gifted students than for poor students. To avoid serious problemsof doubtful reliability, most standardized tests of ability and aptitude in the United States now reportscores in stanines, whioh place students only in one of nine categories on a particular test, The CollegeBoard Examinations, however, still provide normalized item scores,

The laxness of the reliability of standardized tests implies that even a perfectly specified regressionanalysis of the educational prooess would be able to explain as little as 72% of measured student achieve-ment,

The problem of reliability of observational instruments also plagues the measures of the independentvariables, Several critios of major empirical studies have indicated that questionnaires employed toobtain information on student and school characteristiOs have not been validated. The responses obtainedfrom elementary sohool children on parents' educational attainments or trom teachers on their own in-volvement in professional development are particularly suspeot,

The Choice of Aggregation Levels

The discussion of the appropriate level of aggregation over subject matter and grade levels willfocus on three underlying questions, First, at what level of aggregation will the analysis produce themaximum amount of policy information per unit of research effort? Second, what are the consequencesof information loss through aggregation on the policy conclusions of the analysis? Third, what are thestatistical implications of aggregation? The third question will be considered in the discussion of sta-tistical estimation below. The present section will examine the first two questions.

The level of a tgg2_e_gfttio.._eluctttional ror duction function estimation dependsin part upon the goals of the analysis; one must Imow what the policy instruments are in order to estab-lish the proper scope of the study, The recursive structure of the educational system and the inter-relatedness of endogenous and exogenous variables suggest that if one were interested in determiningthe optimal educational programme for a given school, information regarding input-output relationshipsat a fairly detailed level would be appropriate. If one lmows, for instance, what the responsiveness ofthird grade mathematics achievement is to second grade reading skills and arithmetic achievement, thenthe allocations within a school programme could be improved, perhaps with dramatic results, If, how-ever, the only form of leverage over educational practices available to policy makers is the allocationof public funds by district, then the more modest goal of determining the responsiveness of educationaloutcomes to'expenditure per pupil is appropriate. However, even in this case, the researcher mightadd4tionally wish to identify the characteristics of those school systems which are most likely to makeefficient use of additional resources,

tent al information loss thrpugggrgptipn over stO*at_, and grade levels also raisesdoubts concerning production function estimation based on highly aggregated data. It is intuitively ob-vious that first grade reading requires fundamentally different school inputs than does advanced place-ment high school physics. Any educational production function that is estimated from heterogeneousdata will produce a crude average function permitting only questionable interpretation, The analogue

1, Oscar Duros, Mental Measurements Yearbook, Fifth Edition, Highland Park, New ierteyi Gryphon Press, 1966,

6

in private sector empirical production function estimation might be to estimate a function for all manu-facturing; quite obviously the resulting function would not substantially illuminate the question of theemployment effects of greater investments in cotton mills,

While considerable research into the aggregation problem has been conducted, no general conclusionsmay be drawn1 , The problem is essentially one of weighing the additional cost of obtaining and analyzingmore variables against the loss of information or the unsatisfactoriness of more aggregative studies,The concept of aggregation bias has been developed in the context of macro-economic analysis but it doesnot generalize to educational production functions with eases, Because one cannot at present appeal toa well-defined statistical decision theory to Justify a particular level of aggregation, it remains for theinvestigator to evaluate the alternatives intuitively,

SUMMARY

The purpose of this part of the paper has been to identify explicitly some important problems ofmeasurement and conceptualization of educational production function variables, The variables that oneexamines in studying educational production are typically derived variables that attempt to represent thequalitative significance of latent variables but which do so rather crudely; the estimated variables fre-quently are not cardinal measures but rather are ordinal or nominal in nature, The survey and testinstruments employed in examining education are somewhat crude and only relatively reliable; a reviewof the reliability literature indicates that as much as 28% of the variance in output measures might beattributed to the testing instrument itself, Finally, the level of aggregation at which the analysis isconducted determines the interpretation that may be imposed upon the results of the study,

I, H, Theil, "The Aggegation Implications of Identifiable StYuctural Macrorelations", Econometrica, 21,1959o. pp. 14.29,2, H, A, John Green, matzo/1min jugginaAndyilf, Princetom 4,rinceton University Press, 19641 and Walter D, Fisher,

chessimaillittetiojuintit Daltimoret Johns Hopkins Press, 1969,

Iv

STATISTICAL TECHNIQUES FOR PRODUCTIONFUNCTION ESTIMATION

This Part examines the statistical techniques that are appropriate to estimating educational produc-tion functions. In the absence of complicating statistical problems, the appropriate statistical approachto estimating a production function for education would be to obtain least squares estimates of the re-gression equation parameters. The regression coefficients would indicate the marginal or incrementalinfluence of a unit change in a particular independent variable upon the output measure. These coeffi-cients might be, scaled into units of output per dollar, pound or franc of an input and hence might pro-vide direct information on the economy with which a particular input might be employed to increase out-put. The t statistics and standard errors associated with each variable would assess the level ofconfidence that one might place in the estimated parameters. In addition, the coefficient of determina-tion might be employed to indicate the successfulness of the analysis in explaining the educational pro-duction process,

The recursive structure of the educational process, and the problems of conceptualization and mea-surement of educational system variables, considerably complicate the statistical analysis. Two com-plicating factors will be corlidered here, The first is that the recursive model of education becomessubject to simultaneity bias if aggregated over time. The second is that the extensive use of proxyvariables, many of which are qualitative rather than well-scaled, introduces problems both of multi-collinearity and of specification of estimating equations. This section will examine these two factorsof simultaneity bias and collinearity.

The problem of simultaneity bias is introduced into the statistical analysis whenever an output ofthe process appears during the same period of the analysis as an input. The problem of simultaneityis thus intimately related to the question of appropriate levels of aggregation over time. In the presentcontext, simultaneity problems will emerge if the educational period being examined is lengthy enoughto permit successes or failures in learning experiences to become important causal factors in deter-mining the level of motivation and prerequisite knowledge of the student, since motivation and know-ledge are important school inputs as well as outputs.

The problem of simultaneity bias may be confronted in two ways. First, one may, where data andcomputational costs permit, consider the educational process as a purely recursive system. A seriesof regressions for each stimulus-response situation may be estimated with the produced inputs beingtreated as exogenous independent variables in later stages of the process. Simple least squares esti-mation methods then produce unbiased estimates of model parametersl. This approach in additiongenerates a much more complete picture of the educational process and, hence, is much richer inpolicy implications. The second approach is to permit aggregation over time which will create simul-taneous equation bias in the estimated parameters unless more sophisticated estimating techniques

1, H, Weld and L, Juteen, Damanti Analysis, Part 1, New Yorki John Wiley and Sons, 1062,

are used1. The model must be expressed in terms of simultaneous equations in which the structure ofthe process is carefully defined; the output variables may then be expressed as functions of the variableswhich are exogenous to the statistical model. The reduced form equation or equations may be used toestimate the parameters in which we are interested by a variety of statistical methods, including two-stage and three-stage least squares, The computational methods are certain to be much more compli-cated and the results of the analysis much less useful for policy purposes. The advantage of explicitsimultaneous equation methods is that data which are not well suited to highly disaggregative recursiveanalysis may be employ9d to gain some insights into the educational process.

The arises when independent variables used in a statistical analysisare highly correlated. When this occurs there is no way of assuring that the causal influence unique toone variable is not assigned to another highly correlated variable; the problem is one of assigning thevariation in the dependent variable, jointly explained by two or more independent variables, in a satis-factory wr y. This problem is particularly severe when studying educational processes because theextensive use of derived measures of latent variables results in considerable correlation of independentvariables. Socio-economic class and quality of school facilities are examples of variables that usuallyvary together. One procedure for attacking this problem is to employ stagewise regression analysis inwhich the order of regression is specified a priori. The causally prior variable is entered into the re-gression first, and all of the variation in the dependent measure explained by the independent variableand its correlated variable is assigned to the first variable, In effect, the causal ordering of variablesis used to justify assigning all of the explanatory power shared by a set of collinear variables to a firstvariable. When used with poorly specified models and proxy variables, this approach does little to alle-viate the problem of multi-collinearity because the problem remains within the variables used in theanalysis. More detailed specification of the theoretical basis for the estimation of educational produc-tion functions and direct measures of important variables should provide the researcher with insightinto the pattern of interdependence among variables and suggest means of dealing with the pattern2,

1, R, Bentzel and B, Hansen, "On Recursiveness and Interdependency in Economic Models", TJi e Review of Economic Studies,

No, 22, 1964, pp, 163-1 ,

2, Donald E, Farrar and Robert R, Glauber, "Multi-collinearity in Regression Analysis : The Problem Revisited", The Reviewof Bconontatistics February 1961, pp, 92-107,

294

SUMMARY

The central purpose of this paper has been to raise the most important methodological and empiricalobjections to empirical research into the educational production process. The large-scale, non-experi-mental research design employed in such well-known studies as the Coleman and Plowden Reports in-troduces almost insuperable problems into the analysis of the qualitative impact of controllable variableson student achievement. It has been shown that an operational theory of the educational process does notyet exist, Not only do we not have an adequate theory of feasible pedagogical alternatives, but neitherdo we have a theory of administrative choice by which alternatives are selected or by which we mightinfer the normative significance of observed allocations of educational resources, In the absence of atheoretical framework to guide in the selection of variables for analysis and in specifying functionalrelationships among important variants, no causal inference may be drawn from these studies. Theabove discussion has focused upon the validity of empirical research as a source of insights into optimalpublic policies towards education. The empirical research that has been conducted thus far does pre-sent interesting descriptions of many educational systems and offers some highly suggestive correlationsamong school and non-school variables, However, no confidence may be reasonably placed in the policyimplications being drawn from such descriptive research.

The variables which have been investigated in studies of educational technology are not well adaptedto rigorous quantitative analysis. This paper has suggested that the abundance of qualitative and nominalvariables undermines the conclusions that have been reached. The extreme heterogeneity of educationalinputs and outputs and the absence of a plausible scaling of their variables seriously cripple the statis-tical analysis.

The pessimistic conclusions of this paper for large-scale empirical research into educational tech-nology suggest two general approaches to future research, First, one may accept the premise that,suchresearch is highly valuable and attempt to remedy the problems of estimating production functions ibreducation. Second, one may conclude that less ambitious micro level research into educational technol-ogy IP appropriate and endeavour to perfect less ambitious techniques and to enhance the policy value ofeducational research. We will briefly examine the implication of each of these viewpoints.

Application of the empirical production function concept to education demands that the theory ofeducational processes be improved in two important respects. First, the structure of the educationalprocess must be better specified; current educational theory offers only very crude insights into thefunctional form of relationships among educational inputs and outputs, While it is possible to identifyseveral correlates of student achievement, it is not possible to indicate whether thpse effects are linear,additive or independent. The argument that ability and quality of educational experience somehow in-teract is sufficiently appealing not to be summarily dismissed. In addition to our hnprecise knowledgeof the pedagogical process, we are ignorant of the determinants of the implementation of educationalinnovations. Several educators have noted a considerable lag between knowledge of the best educationalpractices and their implomentation. Until systematic research is focused upon the formal decisionprocess in education administration, this issue will remain a question,

68 '

30

li;

Second, as important as the need to develop an adequate theory of education is the requirement thatthe theory be operational. Much of existing educational theory is essentially circular (e, g, definingteacher effectiveness by student achievement), Student ability and motivation are two important variablesthat are also circularly defined, More operational formulations of educational theory by educationists,as well as more objeotive and direct measurement of variables, are necessary before useful applicationsof the production function concept can be made to education,

The alternative approach to enlightening educational policy is to improve the usefulness of micro-level educational research, This alternative has several attractions, As we noted earlier, the moredisaggregative are the analyses, the more policy information may be obtained from the research, Edu-cational changes which are jpriori valuable may be experimentally instituted and the consequences eval-uated. The micro-educational research being suggested has been widely conducted in the form of curric-ulum or instructional evaluation, Several limitations in these common research strategies might beremoved which would, however, increase their usefulness, First, these studies might be improved bydeveloping a corresponding cost-effectiveness analysis; the instrumental variables under considerationmight be scaled by cost in order to indicate the least cost way of augmenting educational outputs. Second,the distributional effects of educational experiences should be evaluated; the conventional evaluationstrategies examine the mean achievements of experimental and control populations, A more sophisti-cated, multivariate statistical analysis would reveal the differential effectiveness of educational proc-esses on students with different abilities, backgrounds or motivations. Third, the results of micro-level educational research might be integrated into a general model of education, Earlier discussionshave stressed the importance of prerequisite sldlls in education, A variety of empirical techniquesexists which might be used to examine the optimal flow of educational experiences, either in order toreduce costs or to maximize the quality and content of student achievement,

In addition to generating more abundant and useful policy information, the micro-level researchstrategy has the advantage of being relatively simply and inexpensive. The limited scope of the analysisreduces the need for elaborate statistical c .mtrols of intervening influences and thereby reduces themagnitude of the sample required to obtain statistical confidence in parameter estimates, The use ofquasi-experimental research designs also reduces dependence on educational theory as a source of

hypotheses.

This paper concludes that policy oriented research into educational technology might be most prof-itably pursued through refinement of relatively conventional, small-scale research designs, The grand,aggregative, production function type of study demands greater theoretical and empirical sophisticationthan education is presently able to provide, This paper also suggests that the policy conclusions beingdrawn from contemporaryiempiricist research into educational technology are not fully supported due tothe defects of the research strategy. These problems are not merely marginal errors in data collec-tion or interpretation but rather reflect the relatively primitive nature of our knowledge of education.These studies of education offer hypotheses and insights into education and, more important, provideindicting pictures of the equality with which educational opportunities are being distributed. The problemof securing a more efficient allocation of educational resources remains to be investigated.

88

Paper 2

PROBLEMS IN MAIUNG POLICY INFERENCES FROM THE COLEMAN REPORT

by

Glen Cain and Harold Wattel

1, This research has been supported by funds ranted to the Institute for Research on Poverty pursuant to the provisions of theEconomic Opportunity Act of 1064, The authors would like to acknowledge the helpful comments received from Dennis Aigner, ArthurGoldberger, W, Lea Hansen, Robinson Hollister, M, I, Lekowitz, Burton Weisbrod and Walter Williams, We are most rateful toMrs, Felicity Skidmore for editorial help,

302

A GENERAL INTRODUCTION

The following paper by Professors G. Cain and H. Watts of the Institute for Research on Poverty,University of Wisconsin, has been included among the papers for this Conference for several reasons.First, the document which has come to be called the Coleman Report1 has been the subject of a majorcontroversy among both academic analysts and governmental policy makers in the United States, Assuggested in several of the papers prepared for this Conference, the Coleman Report has raised ques-tions which are basic to the whole development of educational systems in Member countries. Thus,some discussion of the technical aspects of this controversy seems in order for this Conference. Second,the Coleman Report is significant not only for the particular controversy regarding its conclusions, butalso because of the implications to be drawn from the controversy about the technical procedures usedfor the whole body of studies f educational processes.

Perhaps the most important lessons to be drawn from the Coleman Report controversy are thoseregarding the methodology of quantitative studies of education. It is in this regard that the Cain andWatts paper is particularly rich in insights. They show how the absence of a clear theoretical structureleaves the interpretation of the causal significance of many of the specific variables measured subjectto a good deal of tunbiguity. Further, they not only point out the limitations in the Coleman Report meth-odology, but they also indicate what the requirements are for an improved methodology. Third, Cainand Watts address the problems of method and inference not solely in terms of the requirements ofacademic rigour, as has been the case of most critics of this sort of study in the past, but more ;---ticularly in terms of the use of results in the context of policy decision-making. The points they raisewith respect to policy-related inference extend beyond the Coleman Report, and even beyond studies ofeducation in general, to the area of quantitative inference for the whole realm of public policies. Forall these reasons, it was felt that participants in this Conference should have this paper made availableto them.

1, James S. Coleman et al., Eciality jiLuoltjapaissizaply, Washingtolls United States Office of Education, 1966,

69 33

INTRODUCTION

The aim of the Coleman Report1 is twofold - a) to describe certain aspects of our educational systemand b) to analyse the way it is related to educational achievement - with the objective of prescribing pol-icies to change the system. In its purely descriptive aspects, the Coleman Report presents a very dis-mal picture of the effectiveness of our educational system in securing equal opportunities for all ourcitizens, Looking at educational outcomes for children from different backgrounds one finds wide dis-crepancies which the "American dream" has assumed capable of elimination through the public snhoolsystem. These discrepancies have been authoritatively established in the Coleman Report, and theindictment and challenge they present are a crucial contribution, Although we take a critical view ofthis Report, nothing in our subsequent commentary can detract from the importance of the findings re-garding the inequalities in the education of children of different races, ethnic groups, and socio-economic classes.

Our criticism of the Report is directed toward its analysis, mainly found in Chapter 3, in which anImplicit theory of the determinants of educational achievement is posited, tested, and used to point upprescriptive policy implications, The principal theme of our discussion is that the analytical part of theColeman Report has such serious methodological shortcomings that it offers little guidance for policydecisions, Other critics have pointed to the shortcomings that resulted from non-response to the surveyand from errors in measuring certain variables2 , 3 ; and the familiar uneasiness about interpretingnon-experimental data has been expressed4, Our criticism is more fundamental in the following sense,Even if the survey data were uncontaminated by any biases from non-response, errors in measurements,and an "uncontrolled experiment", there remain the following two basic defects in the Coleman analysis.

First, the specification of the theoreti Iliode 1 is inadequate to support the regression analysisused in testing the model, Little or no theoretical justification is offered for the selection of explana-tory variables, for their functional form, or for the inclusion or exclusion of variables under differentspecifications of the model, Without a theoretical framework to provide order and a rationale for thelarge number of variables, we have no way of interpreting the statistical results. We have no way ofknowing, for example, whether a variable directly represents a policy instrument or is only indirectlyrelated to policy control through some other unmeasured (or partially measured) relationships; orwhether a variable is, indeed, supposed to be subject to policy control or is included in the model toperform a different function. (Examples of this problem are discussed below),

1, James S. Coleman et al, , Equality of Educational Opportunity, op, cit,2, Samuel S, I3ow1es and Henry M, Levin: "The Determinants of Scholastic Achievement - An Appraisal of Sane Recent

Evidence", ayral_ti aunitgasszul, 3, Winter 1968,3, John F, Kain and Eric A, Hanushek, "On the Value of Equality of Educational Opportunity as a Guide to Policy", Discussion

Pa et..A.L.LILQ,3 , togrituaggala Rconcmics, Harvard University, Cambridge, Massachusetts,

4, See the remarks of William H, Sewod, ("Review", AmiglaUziagkcal Review, Vol, 32, No, 3, June 1967, p, 478), ofRobert Nichols, ("Schools and the Disadvantaged", scienceo Vol, 164, eth December 1966), and of Frederick Mosteller in "The

Preliminary Report for Group D", 20th March .1087,

71

34

Second, in those instances where a theoretical justification for the use of a variable in the regressionmodel is clear, the ()Merton used in the Coleman Report to assess or evaluate the statistical performanceof the variable is inappropriate. Instead of providing information about the quantitative effect of a vari-able in altering educational achievement - information wI would enable the reader to assess the fea-sibility and oostliness of operating on the variable - ...dort provides information about a statisticalmeasure of the variable's.performance (namely, its ;:et on the coefficient of determination, or R2, ofthe regression), which gives no clear guidance for translating the statistical findings into polioy action.

The remainder of the paper is organisea around the development of these points. In Part II wecomment briefly on the policy objeotives which determine the choice of a dependent variable - namely,a measure of educational achievement. In Part III, the core of the paper, we discuss the nature of astatistical-theoretical model necessary to handle any analysis of the determinants of educational aohieve-ment. A hypothetical and simplified example is used to indicate a relevant set of questions in terms ofthe objectives of social policy, and to suggest how the results from testing the statistical model shouldbe translated into terms suitable for policy decisions. We should emphasize, however, that the exampleis hypothetical. The most serious gap concerning educational policy, partic,,tarly compensatory edu-cation, remains that of an inadequate theory, and we cannot fill that gap. In Part IV of the paper we do,however, discuss a few of the many specific variables which are found in the Coleman Report to at leastillustrate the points made in our hypothetical example and methodological discussion.

72 35

II

POLICY OBJECTIVES UNDERLYING THE COLEMAN REPORT

A statement of a desirable or at least acceptable objective for social policy is provided by Colemanhimself.

"Schools are successful only insofar as they reduce the dependence of a child's opportunities uponhis social origins. We can think of a set of conditional probabilities: the probability of being pre-pared for a given occupation or for a given college at the end of high school, conditional upon thechild's social origins. The effectiveness of the schools consists, in part, of making the conditionalprobabilities loss conditional - that is, less dependent upon social origins. Thus, equality of edu-cational opportunity implies, not merely "equal" schools, but equally effective schools, whose in-fluences will overcome the differences in starting point of children from different social groups"

The task of translating the objective of equality of educational opportunity into operational terms,however, is a difficult one, The problem is twofold. First, the objective rests on a proposition - thatthe median levels of ability are roughly similar across racial and class groups2 -which canbe assumedbut is not proven, Second, the assessment of progress towards that objective requires measuring in-struments that have yet to be perfected3.

One way to cope with the measurement problem is to rely heavily on the assumption of relative simi-larity in average abilities, On this basis, changes in factors (other than ability) which bring about edu-cattonal achievement may be implemented, and the success of this effort may be tested by achievementscores that are correspondingly averaged over relatively large groups.

Such a focus on instruments of public policy to narrow the gaps between average levels of educationalattainment across racial and economic groups has several implications:

a) The first priority is to develop a model in which the selection of variables is governed by a dis-tinction between those variables which are amenable to policy manipulation and those which are not.The use of non-policy variables may be desirable for 1) stratifying the population if we think thepolicy variables have different effects on different groups, and ii) controlling for intervening effectswhich otherwise may bias the statistical measures of the effects of policy variables. Adding non-policy variables also serves to reduce residual variation (1, e, to increase the 11.2). But with thecurrent availability of large sample sizes this may not have a high priority, particularly since

1, James S. Coleman, "Equal Schools or Equal Students?", The Public lowest, Vol, 1, Summer, 1966, p, 72,2, The median is relatively insensitive to the location of the tails of the distribution - a fact that increases the acceptability

of our worldng assumption, We set aside the question of how the dispersion of the distribution of innate abilities compares across soups,3, A serious obstacle to this approach is that our current measuring instruments are clearly not able to discriminate between

ability factors and achievement factors, The problem of inadequate measuring instruments is emphasized in Frederick Mosteller,"Report of the Harvard Faculty Seminar on the Equal Educational Opportunity Report, Croup A", llth May 1087, pp, 7-8, and JohnP, Kain and Eric A, Hanushek, 2p,a_sk,, pp, 20-21,

7:1

problems of interpreting the statistical results arise as more and more variables are added, someof which inevitably overlap into the role of a policy variable,

b) A possible conflict arises between the objective of narrowing the gap between groups and theobjective of raising the overall average level of each group. Certainly there would be little supportfor a policy which lowered average levels of performance. If, however, our pskillagig evidenceleads us to the assumption that the lower economic groups and disadvantaged ethnic minority groupsare performing well-below their potential, then a policy which seeks to raise their periormanoelevels may be both egalitarian and an efficient way to raise the overall average level of performanceof all the groups combined, (We take up the issue of cost-effectiveness below.)

c) A similar oonfllot between 1) reducing dispersion, and ii) raising the mean level, also existswithin a group, (We should note at the outset that we must expect large variances within groups

relative to that between groups. Every ethnic) and economic group, after all, includes imbecilesand geniuses, stable personality types and psychotics, hard-working students and lazy students,and so on.) A strategy of compensatory education aimed at a disadvantaged group might call forraising the mean level at the expense of widening the distribution, The aoceptability of this out-come would have to be examined in the particular case, but it is difficult to believe that our societyis likely to undertake any policies to cope with between-group differences that will widen (or indeedseverely compress) existing within-group varianee,

d) It may appear trivial to suggest that the variables which serve to represent edueational achieve-ment ought to be carefully chosen and justified, The Coleman Report gathered data on several mea-sures, but fixed on one (test scores on verbal ability) to carry almost the entire burden of the pub-Eshed analysis. If the several tests of achievement are measuring different "outputs", then theo-retical considerations ought to dominate the choice of the most suitable "output" variable, If they

are all measuring the same thing (each one imperfectly) then some, indeed almost any, linear com-bination of the several tests would be better than any one of them,

However, the authors seem to have postulated that one of the tests contained "it", or anyhow moreof "it", and then performed the most remarkable feats of statistical augury to discover which onel .Perhaps other measures would have performed in the same way as the verbal ability test; we will notknow until someone has tried them. But there is no indication that the choice was made on any relevantbasis, and any unique properties of the measure that was used only add to the concern about the inter-pretation of the findings.

I. One Justification for selecting verbal ability was that this variable possessed the largest relative inter-school variances,Another was th,,z among the inter-student variances of test scores, school input variables accounted for more of the variance of verbal

ability than of other test scores, It appears that what underlies thesepuzzling Justifications is a preoccupation with "getting large R2's"

about which we will have a good deal to criticize in Part III, Suffice it to say here that the R2 criterion is not relevant, What isrelevant (but nowhere forthcoming in the Report) is a defence of such a verbal ability test as being a valid measure of educational

achievement which is related, on the basis of a hypothesis concerning dm determinants of educational achievement, to a specified setof school input variables, Instead, the fact that the verbal ability test is less likely to be affected by the variation of school curricula

and instruction than are some of the other tests is offered as further Justification for settling upon the verbal ability test I (Sees lames

6, Coleman, et al, , !pant of 110:z_tal. Opportunity, inst.. pp, 203 ff, ),

74

III

A SUGGESTED APPROACH TO MEASURING THE DETERMINANTSOF EDUCATIONAL ACHIEVrMENT

The following points about the analysis of specific variables as determinants of educational achieve-ment Lre developed in this section, The role of a variable in affecting objectives can only take on meaningand be interpretable in the context of a carefully specified and theoretically justified model, When wehave such a model in the form of a regression equation, the regression coefficient is our most usefulstatistic in measuring the importance of the variable for the purposes of policy action,

a) The Issue of the Significance and Importance of a Variable

ln the analysis of the relation of school factors to achievement, the principal statistic offered inevidence by the Coleman Report is the per cent of variance explained. As indicated in their methodol-ogical appendix, this is because the authors are interested in assessing the "strength" of various re-lationships, and they believe that the per cent of variance explained provides the best general purposeindicator of "strength". It will be argued below that this measure of strength is totally inappropriatefor the purposes of informing policy choices, and cannot provide relevant information for the policymaker'.

Consider a general function expressing a relation between y and several x's, y f (x1, x2, xk).

What conceptuai framework can be used to discuss the strength of the relation of y to, say, x2? If we

are liinited to the information provided by the function f (x1, x2 xn), the partial derivative by/8 x2 f'2 (xi, x2, . xn) is both simple and complete. In the case of linear functions, the partial

derivative is a constant and expresses the change in y induced by a unit change in x2.

It should be clear that a change in the unit of measurement will change the magnitudu of such deriv-atives, and that any comparison among them must establish some basis for comparability among theunits of measurement. In the context of an analysis of the relation of school factors to pupil achieve-ment, it would seem evident that our interest lies in purposive manipulation of the x's In order to effectan improved performance in terms of y. We can, and should, ask for the expected change in y inducedby spending some specific amount of money (or political capital, man-hours, etc, ) on working a changein x

2say, as compared with the alternative of spending the same sum on x3. Budgetary cost is not

1, That the main purpose of the Coleman Report is to serve as a guide to policy action is made explicit and emphasized repeat-edly byt James 8, Colcnan, "The Evaluation of Equality of Educational Opportunity", Re ort 25'litar for dui Study of the.Social Oronization of tiohools, Johns Hopkins Univeksity, 1968.

75

tAto 38

necessarily the only basis of comparability. But unless some such basis is defined, and its relevanceto policy explained, the question of "strength" has no meaning.

What basis of comparison among the x's is implied by the per cent of variance explained - which isthe indicator of the "strength" of a variable used in the Coleman Report? To answer this question wewill corsider the common case of a linear function, the only type of function investigated in the Report.

The ordinary partial regression coefficients, bi, for I = 1, 2, , k, represent the partial deriva-tives of y with respect to the several x's - where each x is measured in some conventional (perhapsarbitrary) unit, As indicated earlier, some adjustment of these derivatives is generally required inorder to establish oomparability. By using the per cent of variance uniquely explained by xi, call it

, as the measure of strength, the authors have implicitly assumed that x's will be render4d compara-ble by measuring them in units corresponding to the orthogonal (or uncorrelated) part of their respectivesample variances, It is easily shown that:

s2

bi

=2

x(1 - R2

i)

as2

where the s symbol refers to the sample standard deviations and R2 is the coefficient of multiple de-af

termination for the "auxiliary" regression of xi on the other (k - 1) of the x's' Thus,i

represents

the square of the regression coefficient which would have been obtained if:

a) each of the x's had been divided by its standard deviation discounted for its relation to othervariables, and

b) y had been divided by its standard deviation, i, e,

* 2

93i

(5xi*

where y* +31 and x*i =

1. What we refer to as thetpi statistic is labelled the "usefulness" measure of the ith variable (denoted byP2y,

xi(p))in Richard

B, Darlington, ("Multiple Regression in Psychological Research and Practice", eachologis.11 t_i_Metin, Vol, 69, No, 3, 1968, pp, 161-182, whose discussion of this statistic parallels much of ours and suggests several references for the interested reader, He uses:

2

2

s

(p)

$1) y.b

x1(p)

s2

where s2 , (p) is the residual variance of xi, 1, e, the variance of xi after controlling for all other x's in the multiple regression. Hisxi

s2 , (p) is precisely equal to our s2

Rai), and was shown in this form for the special case of a multiple regression w4th two predictorxi xi

variables, (See equation (6) in Darlington, oo, cit, ), The expression, Rai, is the same statistic as the C2

referred to by James 8,2

Coleman, ("Squality of Educational Opportunity", ournal of Human Resources, 3, Spring 1068, pp, 241-242) in his reply to thecomment by Bowles and Levin (op, cit), Note, however, that Coleman's definition of the "unique cLittibution" of a variable, which

involves C2, is in ertor unless the variable whose. contribution is being assessed has a unit variance,

6ia

It seems very difficult to find a reason why x's measured in terms of dependency-discounted-deviations, or "3-D's", are comparable for any policy purpose, Is a 3-D increment of xi equally costly,

equally feasible, or equally appealing to the Congress as an increment of x2? Is there, indeed, any ba-

sis for arguing that these 3-D units form a relevant set of policy alternatives such that one would havethe slightest interest in how the several variables rank according to 0i?

It should be clear that measuring "strength" by the usual regression coefficients, or by the Betacocificients1 , is in general no better than using 0. Whether the variables are scaled conventionally orby some equally arbitrary sample-generated unit, they will usually have to be readjusted to securecomparability in the context of a specific choice problem. (This task is usually simpler if the conven-tional scale has not been altered, and it is more likely to be recognized as a necessary step in the anal-ysis2.) Although the discussion above was in terms of single variables in a given function, analogousarguments hold for groups of variables, or for the same variable in functions describing relations fordifferent groups, regions, years, etc.

How did the choice of such an odd measure of "strength" come about? A plausible explanation isthat the investigator is focussing on the "statistical significance" of the relationship. In fact the F-ratiotest statistic, which is commonly used to test the hypothesis that one or several coefficients in a linearfunction are equal to zero, is very simply related to 0. When a single coefficient is tested, the F-ratiois strictly proportional to 0:

(t-k-1)F1, t-k-1 -

1 - H2

where t = sample size, and k = number of independent variables in the regression.

Where F is greater than some critical value, one commonly reports that the variable in questionis significantly greater than zero at, say, the . 05 level. All this means is that in order to maintain abelief that the variable in question has absolutely no effect, one must believe that the sample analysedhas surmount& odds of 20 to 1 by showing such a large apparent effect, Clearly, the greater is y3i or

F, the greater the statistical significance and the harder it becomes for a betting man to stick to the

i, Note that:

t. B2 (11 1 al

If there is only one x, 1, e,

r2

el 161

k

22

1, or

82i

2if xi is orthogonal to all other x's, the term involving Rai drops out and we have:

sx,

b It the squared Beta coefficient,is2, Indeed, an important advantage of the ordinary regression coefficient, bi, is that the effect of a unit change in xi on y is,

as a matter of course, translated by the user of the statistics into terms relevant for his decision context, It has been suggested thatpublication of the regression coefficients produced by Coleman's research would lead to reckless and irresponsible interpretations("Equality of Educational Opportunity: Reply to Bowles and Levin", , p, 240), This must be because either the statisticsthemselves or their interpreters are untrustworthy, If the problem lies with the statistics, it is hardly more responsible to publishstatistics which are better behaved simply because they are definitionally limited to the positive numbers between 0 And 1, withoutrevealing the more suspicious-looking Joint products of the analysis, If the problem lies with the analysts, why give them anystatistics at alit

7?

40

belief that the partial derivative is zero. This Is surely a very restricted and specialized meaning of"significance", since it may bear no relation to the significance (1, e, importance) a variable has forpolicy purposes1 ,

When the regression model has included all the independent variables, the F-test (or related t-test)of the "net" or "partial" coefficients is not, of course, affected by the order of introduction of the vari-ables into a stepwise calculation of the regression. But, the effect of a variable or set of variables(however "effect" is measured) will show up as different in the case where another set of variables is"held constant", from the case where there is no control over that other set. The only exception is whenthe variables to be controlled are uncorrelated with the set being examined, but this situation is presentso rarely in non-experimental data that it can be dismissed°,

When there is a legitimate interest in testing the zero-effect hypothesis, one of the variants of Va.,F-test is available and nothing else will quite do. There is an entirely unwarranted tendency, however,to use the F-statistic (or its cousin 0) to indicate the more relevant kind of policy significance. To takea homely example, one might suppose that height and sugar consumption are both related to an individual'sweight (among other things of course). In most contexts, height would explain more variance than sugarconsumption. But to a person embarking on a weight-control programme this is not the important fact.Anyone who would seriously entertain the hypothesis that weight does not depend on height has more blindobjectivity than most of us - but such a person is the only one who should care about the relative size ofthat test statistic, It is easy to imagine an interest in a test on the "sugar effect", but why say that itis less important or significant or strong, just because it explains less variance?

A second possible defence for the practice of evaluating variables by 0i lies in its similarity to the

Beta coefficient. The use of such "standardised" regression weights is usually predicated on an assump-tion (rarely made explicit) that the sample standard deviations used for adjusting the regression coeffi-cients indicate a relatively fixed range of variation for the several variables. There is, in other words,some notion of "normal" limits of variation which are related somehow to the variation actually found ina population. If some x shows little variation in a representative sample drawn from an interesting popu-lation - the argument goes - then we must reduce its coefficient in order to achieve comparability withthe coefficient of another x that has a larger variance,

The use of 0i for comparing tne effects of variables can be interpreted as the result of following this

same logic farther into the labyrinth of least squares regression algebra. Specifically (as seen bythe f)rmulas on p, 76, the standardisation involved in 0i is in general sensitive to the sample variances

and inter-correlations for all the x's in the regression. Such a standardisation is of interest only if onefeels that the entire joint distribution of regressors is both fixed in the population and well representedby the sample,

1, When 0 is properly interpreted as a test statistic, one must keep two things in mind, a) Its relevance is limited to the zero-effect null hypothesis and b) that, as in all hypothesis tests, the power of the test is as important as the level of significance, A bodyof data may be unable to reject the hypothesis that some coefficient is zero, and be equally consistent with a hypothesis embodying amiraculously high effect, Alternatively, a very powerful test might reject the zero-effect hypothesis, and also reject a hypothesis thatthe effect is large enough to warrant any further interest in a variable,

2, An extensive controversy concerning the order of variables has appeared in the literature*, But neither critic nor defenderhas presented an adequate theoretical framework within which the objects of their dispute become worth arguing about,

- Samuel S. I3owles and Henry M, Levin, "The Determinants of Scholastic Achievement - An Appraisal of Some RecentEvidence", 24..01,

- James S. Coleman, "The Evaluation of Equality of Educational Opportunity", okt.s.a.- James 5, Coleman, "Equality of Educational Opportunityi Reply to Bowles and Levin", 221.911,- Marshall 5, Smith, "Comments on Bowles and Levin", Journal of Hump tlesorts, Vol, III, No, 3, Summer 1068,- Samuel S, Bowles and Henry M, Levin, "More on Multicollinearity and the Effectiveness of Schods", Jojyakl_sthat_nan

Resources, Vol, III, No, 3, Summer 1968,- John F, Kain and Eric A, Hanyshek, "On the Value of Equality of Educational Opportunity as a Guide to Policy", mak,

78

There are many contexts, particularly in the natural processes studied in the physical sciences,when the persistence of specific sizes of the variances and correlations arrong some of the variablesmay be a warranted assumption. But it is patently absurd to postulate such invariance for variablesthat can be affected, directly or indirectly, by the policy alternatives that have motivated the analysis.

The use of Beta coefficients (standardised only for variance) is subject to the same sort of criticism -they retain their meaning only so long as there is no intervention by man or nature to change the variancesused for standardisation, But where B is only crippled as a guide to policy,

1

is totally disabled, The°

latter maintains its relevance as a description of a relationship only if we stand aside and wring our hands,

b) A Hypothetical Numerical Example

A number of the points discussed above can,be grasped most readily by a review of a simple numer.ical example, Suppose that the relation between a suitable measure of school outcomes y , and indexesof sehool quality x1 and non-school background and 3nvironment x2 , is as follows:

y = 1 + x1 + 2, Ox2

+ u

The constant term reflects an arbitrary choice of origin for the outcome measure, and we assumethat x

1and x2 are standardised scales with zero means and unit variancesl. The final term, u, is an

unobserved disturbance term which must, in part, reflect measurement errors in y and other relevantfactors such as "native ability" (whether genetic or irreversibly determined at some earlier time), Thisdisturbance is defined to have a zero mean and to be uncorrelated with x1 and x2, (Assuming that x

1and

x2 are uncorrelated with u, either singly or in a linear combination, permits us to accept the regression

coefficients as unbiased moasuros of the effects of x1 andx2'

he variance of u is arbitrarily set at

unity,

Now consider several alternative situations which reflect different policies with regard to the allo-cation of the composite bundle of factors which determine school quality, xi, For greater simplicity we

will not consider allocations that change the variation of x1 over schools, Only the degree, and sign, of

the correlation between x1 and x2 (p12)

will be changed, To make the policy more concrete (and more

obviously hypothetical), suppose that all schools have wheels so that a fixed population of schools ofvarious qualities can be moved around to serve an equal number of communities. A zero correlationbetween x1 and x2 (012 = 0) would result from a random assignment of schools to communities. It

would be changed to a positive value by moving some of the better schools from "bad" communities (asmeasurcd by x2) to "good" ones, and vice versa, Similarly, 612 would become negative if the bad corn-

munities swapped their bad schools for good onbs fromthe good communities. 012 would anproach 1, 0 if

the "best" school served the "best" community, the second best school the second community and so on.

Any alteration in the way input variables are combined will change the distribution of the outcomes;for instance, a change in the variance of y is a necessary result of a change in the correlation betweenx1 and x2' given our specification of constant variances of x

1and x and constant effects (b,$) of x

1and

2 .

x2, Table 1 shows the consequences for several parameters when the correlation between x1 and x2

takes on several different values, ranging from 1. 00 to -1, 00.

1, These scalings merely simplify the numerical calculations and interpretations of the example, It sould be noted that Anne y is notsimilarly standardised, there h nothing at all unconventional about a coefficient of two for the second independent variable,

42

Table 1. CONSEQUENCES OF VARYING CORRELATION BETWEENREGRF,SSOR V,allABLES IN A SIMPLIFIED REGRESSION MODEL

Model: y = 1. 0 1. Oxi + 2. Ox2 + u

ax2 ax2 .a2 = 1 01 2 u

Pux1

ux2

= 0' 0

ROW

NUMBERPARAMETERS I U III IV V VI VU

1 p 1. 00 . 90 . 50 0, 0 - . 50 - . 90 -1, 00

2

2 P12 1. 00 . 8 1 . 25 0. 0 . 25 . 8 1 1, 00

3 (72Y

10, 0 9. 6 8, 0 6. 0 4, 0 2.4 2. 0

4 p 2. 900 . 712 . 500 . 167 0. 0 . 2671 . 5001

"1.

5 P2

yx2

, 900 . 876 . 782 . 666 . 563 . 505 . 500

6 R2y x1x2

. 900 . 896 .875 . 833 . 750 . 583 . 500

7 01 0. 0 , 020 . 093 . 167 . 187 . 078 0, 0

8 02 0, 0 . 184 , 375 . 666 . 750 . 316 0, 0

9 R2yx1 . x2

0. 0 . 160 . 429 . 500 , 429 . 160 0. 0

10 R2yx2 . xi 0. 0 .432 . 750 . 800 . 750 . 432 0. 0

11 131

. 312 .327 . 354 .408 . 500 . 645 . 707

12 B2 . 624 . 654 . 708 .816 1, 000 1, 29 1, 114

13 b1

1, 00 I,. 00 1, 00 1. 00 1, 00 1, 00 1. 00

14 b2

2, 00 2. 00 2, 00 2. 00 2. 00 2. 00 2. 00

1, The squared simple correlation coefficiencies shown here are squares of negative values for pyxi. All other values for Pyxt andin the table are positive.

Pyx2 _

80

43

In column IV one finds the simple case when xi and x2 are uncorrelated - schools have been assigned

to communities at random. The variance of y (a?) is equal to 6, 0, and this partitions nicely into a com-

ponent due to school differences with variance 1, 0, another component due to community differences withvariance 4, 0, and a third due to the combination of factors accounted for implicitly by the disturbanceterm with variance 1. 0, The two variables, xi and x2, together account for 5/6 of the variance - 1/6

for xi and 2/3 for x2 - as shown in the entries for the simple squared correlations (p2D2 ) and the

yx1 yx2squared multiple correlation, R2

y .x1x2

Because x1

and x2 are uncorrelated (orthogonal), the incremental fraction of' explained variation

that i6 obtained when x say, is added to the regression (0 = R2 D ) is equal to the2

1, ,1 y. x

1x2 yx

2

fraction explained when x1 is used alone (p2 ). The same is true for the increment due to x2.yx

1

The squared partial correlations are obtained by dividing the increment due to xi, say, by the

fraction of variance left unexplained by x2:

2

pyx1. x2

01

1

R22

y,x1x2 x2

1 n2r yx2

The Beta coefficients, Bi, are simply the partial regression coefficients divided by the standard

deviation of y, ay, and multiplied by the unitary standard deviation of xi. The partial regression coeffi-

cients shown in the last two rows are constant, of course, because the populations have been generatedby maintaining that assumption, (Columns I and VII, where xi and x2 are perfectly correlated, are

limiting cases - the multiple regressions would be impossible to carry out with data generated fromthese cases.)

The values of the various parameters listed in the columns of this table must be regarded as"population" values. A limited sample drawn at random from one of these populations could produceestimates of these parameters which would differ from the "true" values by sampling errors of theusual sort.

If the allocation of x1

is changed from a random one by matching "good" schools with "good" communities ,

the correlation between x1 and x2 becomes positive. Moving towards the left from column IV in the table , one

finds first that the variance of y gets larger. This is intuitively explained by thinldng of the schools as

reinforcing and intensifying the inequality found in the environments, The simple correlations shown

in the fourth and fifth rows both increase as the two variables become increasingly good substitutes foreach other, and the multiple correlation goes up because the constant amount of unexplained variance(from u) becomes a smaller part of the whole variance of y .

81

44

The incremental explanatory power or "unique contribution" (measured by 0i) declines as p12 in-

creases from zero, and 0 reaches zero in the limit where p12

= 1. The squared partial correlations

display badcally the same pattern. Both are transparent consequences of the increasing interchange-ability of xi and x2 - as their correlation increases, having both adds very little new information,

Finally, the Beta coefficients decline as a consequence of increases in variance of y, Any deeper mean-ing of this change must be supplied by those who have a penchant for using this scaling convention.

Consider now the consequences of allocating relatively more "good" schools to the "bad" locationsand vice versa. As p

12falls from zero to negative values one finds the variance of y falling also, (See

columns IV to VII.) Here the schools compensate for, or suppress, the inequality produced by unequalbackgrounds,

The squared simple correlations, p 2, both fall initially; p 2 going to zero at p12 = -0.51,yx1 yx1

The variance explained by x2 falls steadily until at the limit it explains only half of the (smaller) variance

of y. Beyond p12 = -0. 5 (in columns VI and VII) the simple correlation of xi with y becomes negative,

and in the limit it is simply a mirror-image of x2 and thus has the same squared correlation,

The squared multiple correlation falls as the "unexplained" component of the variance becomesrelatively more important, The net or unique contributions, 0i, are seen to reach a peak at p12- -0. 5

and then to fall once more to zero as.x1 and x2 become more identical. The squared partial correlations

are seen to fall quite symmetrically on both sides of column IV where p = 0.

Finally, the smaller variance in y brings about an increase in the Beta coefficients, By this mea-sure the effects of both x1 and x2 become more and more powerful; by contrast, the regression coeffi-

cients measuring their effects remain unchanged at their assigned values.

Now consider a not-entirely-hypothetical society which has shown some tendency to place as "best"schools in the "best" places and to direct its "best" efforts toward its "best" pupils, This produces anp somewhere between 0, 5 and 0.9 - like columns II or III, An educational survey might very well

find that background and environment are 4-10 times as strong as school quality if it looks at the relativesize of the Less extreme, but no more relevant, statements could be made by comparing the b's or

B's. But what is the purpose of such comparisons? If the survey is large enough to get decent estimatesof the b's, its authors could observe b1 and infer that school quality does make a difference. It follows

that moving some schools could change p and shift the society's educational process toward one de-

scribed by columns V or VI, Such a reallocation would substantially reduce the inequality of outcomesand attenuate ale correlation of outcomes with social origins; and it would seem to be a proper sort ofalternative to considor when interpreting the results of an educational survey.

It must be heavily underscored that, in terms of the model reviewed above, comparisons of therelative explanatory strengths of the two variables xi and x2, whether one uses simple, partial or

multiple correlation coefficients, unique contributions or regression weights, adjusted or not, a

1, Intuitively, whenp12 - -0,6 we can think of the positive contribution of xi to explaining variation in y being exactly negated

because of the negative correlation between xi and x2. As the negative correlation between xi and x2 gets larger in absolute value than

-0, 61 the true positive. effect of xi h more than offset in the simple relation between xi and y (when x2 is not held constant),

.82

45

pointless, if ono is concerned with assessing the possible effects of educational policy, compa)Asons ofany kind with the effect of "control" (1, o, non-polioy) variables are silly. Moreover, all the statisticsinvolved in the comparisons, except for the unadjusted regression coefficients, are dependent upon theparticular policies pursued when the data were collected. Their use runs the risk (,f declaring a policyfeeble simply because historically it was not vigorously applied.

In the example shown in Table 1 the "best" allocation to achieve equality calls for a perfect negativecorrelation between xl and x2. By this aliocadon the variance of y is reduced to a minimum (-2), It

should be noted that educational policy might also ohange the mean and/or the variance of x1,. With these

added degrees of freedom it would be possible, in principle, to eradicate all gross association of 3 withx2, and - as an added option - reduce the variance of y to the absolute minimum introduced by the un-

observable variable u,

c) The Need for a Theoretically Justified Model Relevant to the Palley Context

In general terms one may view the Equality of Educational Opportunity Survey as providing infor-mation on the joint distribution of a large number of variables, The analytical effort should be directedtoward answering questions about how new or altered policies (more partioularly educational policies)would change various characteristics of that joint distribution either directly or indirectly, To do this,one must have a consistent and complete set of specifications concerning: i) which characteristics ofthe joint distribution are constant, ii) which can be changed directly by specific activities (policies),and iii) which ones must therefore be determined by the assumed structure and prescribed policy.

This set of specifications is commonly termed a theory or model, In the Coleman Report there isno explicit discussion of a consistent theory of this sort, Some theory, of course, must underlie anysort of policy prescription, It is not that one can choose to draw conclusions from the objective factsalone, without the aid of any theory, but that if one leaves the theory implicit, ambiguous and obscure,contradictory possibly nonsensical or even self-contradictory premises go unnotieed.

The theoretical structure of tue simple model discussed above asserts that the functional relationbetween y and xl, x2, and u, can be approximated satistactorily by a linear and additive function, with

coefficients that would remain fixed under policies designed to change the distribution of x1 and/or x2,

Similarly it is assumed that the mean and the variance of the disturbance variable, u, will be unaffectedby polk les aimed at affecting y via x1 or x2, The objective of policy is taken to be some optimal com-

bination of high average level of outcomes (mean of y), minimal inequality (variance of y) at least asthe variance or inequality is affeotedby inter-group differencos - and easy class mobility (minimal cor-relation of y and x2).

The tools of educational policy are taken to be measures that would shift the mean of xl, compressor expand its variability, and/or revise the correlation between xj. and x2. If one wishes to consider

social policy more broadly, similar alternatives for changing the distribution of x2 would be available.

Within the structure so far specified it is possible to deduce the effects on tne marginal and conditionaldisti"ibution of y for any particular change in the x

1or x2 distributions. If no further restrictior

relevant information is added, any particular goal in terms of the basic objective can clearly be achievedby a wide range of different manipulations of the x1 anti x2 distributions, The question of relative strength,in the sense of ability to manipulate y, can now be seen to be meaningless - rememberirAg that the scalingof x

1and x2 was arbitrary to begin with. Each of them can be used to achieve the objective so long as

unlimited freedom is available for changing the mean, variance and correlation. If x2 is not manipulableby educational policy, on the other hand, who cares how effective it might be if it were?

8461,

Consider, however, a very simplified situation in which the objective is to close a substantial gapbetween the mean value of y for negroes and the mean for whites. Assume that the function above holdsfor negroes, and that one's policy choices are limited to changing - at most - the mean value of xi and

x for negroes, Which policy or combination of them one chooses will depend on further information

about the costs of each alternative. Costs may be in terms of dollars, time, political consensus or allthree - but must be made explicit.

Indeed, oile might, for purposes of policy analysis, scale the variables available for manipulationso that a unit change in xi is an equally costly (or time-consuming or consensususing) alternative to

change in x2, If an "Iso-chunk" of xi is defined to be a $1 billion worth, each one must be a fifth as

large as the original unit costing $5 billion - hence its coefficient must be 0, 2 (1. e. the old bi = 1 coef-

ficient multiplied by its now unit of measure, 0. 2). Similarly, an "Iso-chunk" of x2 is only four per oent

of an original unit priced at $125 billion, and hence its coefficient must be 0. 08.

Several variations on the "Ise-chunk" idea can be specified. Take as given the relation between"output", y, and "inputs", xi and x2;

(1) y = a + blxl + b2 x2 + u

Suppose first that the "costs" of alternative mixes of x1

and x2, in terms of any scarce item onefinds important, are given by;

(2) C c1x1 + o

2x2

One may now rewrite equation (1) in terms of "Iso-chunks" which correspond to the amount of xiarrived at by using one unit of whatever "cost" consists of - dollars, man-hours, class-hours;

and

x =1x

11

x'2 2

x2

Thus, "Iso-ohunks" (read dollars or hours) of C spent in changing xi can be substituted in (1) forthe xi;

(3) y = a + B x'1

+ B2

x2 ' +1.

hiwhere Bi - oi

We may call these Bi "bet coefficients" - derived from Israeli pronundation of the Hebrew name

for the co.responding alphabetic character'.

The bet coeffieients give quite direct answers as to which use of the scaree item C yields the largestincrement in y. To the extent that relations (1) mu (2) adequately reflect the way the world works, one

1, Professor Azilwr 3, Goldberger coined this felicitous terminology,

could confidently proceed to acid to the existing educational process by directing all available C Into thexi for which B

Iis the largest,

Unfortunately, one does not usually have that muoh confidence in a couple of simple linear relations,Commonly, relation (1) will be estimated on the basis of a limited sample, and one's confidence in ex-trapolations beyond the range of observed combinations of xi and x2 deteriorates rapidly''. Moreover,

one would rarely encounter a "cost function" as simple as the one in (2) = i many there will be diminishingreturns causing marginal oosts to rise beyond some point, Bet coefficients derived as above ought,therefore, to be interpreted as reflecting, at best, the relative effectiveness of variables in that vicinityof the data over which a linear approximation is deemed to be "sufficiently accurate", taking into aeoeuntreservations about both relation (1) and relation (2).

1, This information on the reliability of the estimate is given by the confidence interval computed for the bet or regessioncoefficient, Our emphasis on the expected value of the Di (or bi) does not imply that we believe a dechion maker would have no

interest in the confidence interval. Mead, one can imagine cases when a dechion maker has some asymmetric subJective utilityweighting scheme such that zero or negative values would be deemed so critical - more than offsetting the equally probable highpositive voiltes - that a Di which was (slightly?) lower than a 132 would still be selected if the confidence interval of 13

1were suffi-

ciently tighter. Such cases ought to be explicitly argued, however. This proper usage of the confidence interval does not wa..rantusing the statistics, instead of the bet coefficient and classical inferences about it, as the primary criterion of policy choices,

85

48

IV

INTERPRETING SPECIFIC VARIABLES IN THE COLEMAN REPORT

The absence of any explicit theory of educational achievement is the chief source of the difficulty ininterpreting the statistical results of the Coleman Report. We can illustrate the problem by discussingsome of the variables used in the Report.

a) Attitudinal Characteristics of the student

One remarkable finding of the Report's analysis is the high partial correlation of fate control/per-sonal efficacy variables with the verbal ability score used as a measure of educational outcomesl, Therelation was particularly strong (by the Report's criterion) among minority group children. Without atheory, however, we cannot answer the following types of question:

1) Is this variable itself merely a reflection of (perhdps "caused by") educational achievement?One can easily imagine situations in which educational accomplishment would instill confidencein a youngster and produce a high score on the measure of this variable°.

2) Is this variable important only because it is related to various objective factors about thestudent's family, cnmmunity, and school environments, which are not fully measured in themodel, and which "really" explain both school performance and the fatalism score? This setof relations would again be quite plausible on a priori grounds 3

tinder situations (1) and (2) above, we can say no more than the follow:1g. Either changes inthe variable, "control over one's fate", are unattainable unless performance on the otherobjective variables is changed; or, if some change in the score could be induced (by, say,counselling), there is no reason to believe educational performance would change.

3) What if, contrary to (1) and (2), the fatalism variable is a personality trait that does have aseparate influence on educational achievement? We still need to know how policy can changethe trait to make use of our finding. Clearly these attitudes may be quite congruent with anobjective assessment of the situation children find themselves in. If so, the school may beseverely limited in its ability to reorient such attitudes (one may have to reintroduce prayer).

1, A number of questions in the survey attempted to measure the student's sense of control over his environment and his senseof fatalism,

2, Precisely this specification of the oausal relationship is put krwarcl int Alan Wilson, "Educational Consequences of Segre-gation in a California Community", in Racial Astitatikylkblio Schools, United States Comrnislion on Civil Rights, Washington, GPO,1961, Vol, 11, pp, 192 and 200,

3, The report explicitly notes that the simple correlations of verbal ability and the fate contol variable are similar to the inter -correlation among the achievement variables, A finding which seems consistent with the interpretation that these attitudinal variablesare Just another means of measuring the Joint output of school and non-school processes impinging on a child's development*,

James S. Coleman Isignality.of tjalipatamally, p, 319,

49

A verdict of helplessness may have to be passed on the schools, But the evidence in the reportsupports it neither by adding to our knowledge of the causal relation nor by indicating a low pay-off from interventions within that relation,

b) Charaoteristics of the Student's Peer Crotty

In a review of the Report's findings, Harry C, Brodemoier notes; "More important than all sohoolcharacteristics and teacher quality for negro students is the degree to which the other students in theirschools have the following characteristics; their families own encyclopedias, they do not transfer moil,their attendance is regular, they plan to go to college, and they spend rather much time on homework"1He notes in a footnote, "I assume no one will infer from this that the solution is to put encyclopediasin everyone's home",

But, is such an inference less satisfactory than making no inference? Is it any more naive than thepresentation of the vague theoretical framework that permits us almost no grounds for saying how weshould interpret the "significant positive coefficient" of the encyclopedia variable? Consider the follow-ing' interpretation;

Encyclopedia ownership is a variable that indicates an intellectual atmosphere in the home conduciveto schooling, and/or a measure of affluence that is not fully captured in other measures (of affluence)in the model, and/or a measure of parental attention or affection that contributes to the student'semotional stability and, thereby, to school performance - any or all of which factors oreate thepositive peer group influence,

Presumably, this interpretation is "more sophisticated" than the inference Bredemeier noted, Butis it more helpful? Indeed, what our hypothetical theory has told us up to now is that; 1) if it is intel-lectual atmosphere that underlies the relation, the variable has probably no policy significance sincewe do not know much about changing intellectual atmosphere, If we thought we did !mow something abouthow to make the change, we would need to know the specification of the reit tion between encyclopediasand intellectual atmosphere, ii) If it is affluence that underlies the relation, then we need to ask ourtheory to translate a unit of encyclopedias to a unit of wealth (or income flow) so that we know how muchof a change in income will be necessary to yield the changes in educational performance.

We could continue these "if" questions almost indefinitely; but let us summarize the function of ourhypothetical theory by saying that it has forced us to consider the possible tortured interpretations wehave to make, or preposterous policy actions we might have to follow, as a consequence of such cavalierinclusion of ad hoc variables in our model.

c) Environmental Characteristics

The Coleman Report stressed that the influence of the regional and urban location of the school andthe socio-economic status of the student body in the school were highly important in explaining a student'seducational achievement. A theoretical proposition underlying the authors' interpretation of this findingwas that the environment is exogenous and "causally prior" to such factors as school resourc .s; so thatan appropriate procedure was to enter the former variables, note the contribution to R2, and then addthe school resource variables and observe their additional contribution to R2. Other demurrers to thisprocedure, quite apart from the issue of the R2 criterion, may be mentioned.

If families select their residence on the basis of the quality of school, residence is neither exogenousto the process nor causally prior to the school resources variable. Particularly with regard to the racialcomposition of the school, the phenomenon of selective migration may be confounding the results. For

1, Hairy C, Deeds:mein, "Schools and Student Growth", April 1D6C, p, 29,

88

50

example, if a large percentage of whites in a school or a large percentage of high socio-eoonomio groupsappear to have a positive effect on the educational performanoes of negroes or low SES groups, we shouldconsider the hypothesis that the latter fEunihes have strong "tastes" for a high quality eduoation for theirchildren and have moved to a district whore the school has a favourable reputation. The observed posi-tive effect of the environment on the educational achievement of disadvantaged groups may therefore beoverstated, since some of the effect stems from the unmeasured personal traits of the families; it isfurther possible that some effect is attributable to the beneficial resources of the schooll

What theory of educational achievement justified "urbanness", "Southernness", etc. , as oausalfactors - except insofar as these traits are related to such specific) variables as the family character-istics and quality of schools found in these areas, There is a real danger that such location variablesserve only to attenuate the influenoe of other variables, of interest when such other variables are un-measured or measured with a large error component.

d) Teacher Quality

One type of v.4riable that belongs in the category of sohool resources over whioh we have some de-gree of policy control is "teacher quality" - itself a composite concept made up of several variables.The conclusion in the Report about teacher quality appears to strike a rare optimistic note regardingthe beneficial influence school resources can have in compensatory educational efforts. The Reportstates on page 317 that "a given investment in upgrading teacher quality will have the most effect onachievement in underprivileged areas". Surely, the theoretical justification for this variable shouldbe quite firm, Moreover, the wording of the Report's conclusion exactly fits the criterion we haverequested for assessing each variable.

Unfortunately, the statistical evidence in support of the finding the authors present concernsII variance explained", "Given the fact that no school factors (excluding student body composition) ac-count for much variation in achievement, teachers' characteristics account for more than any othe:'. "And, "by the 12th grade, teacher variables account for more than nine per cent of the variance amongnegro students, two per cent among white students" (page 326). It is perhaps superfluous to mentionagain that this ranking of importance of a variable in terms of variance explained does not tell us whatthe "bet coefficients" are, nor permit us to derive them; therefore, the conclusion about a "given in-vestment in upgrading teacher quality" for underprivileged areas is not supported. If, foi example,the variance of verbal ability were large among teachers of negro students and the educational achieve-ment PnAres had a relatively small variance, the high partial correlation coefficient (and 0) of thisvarhtwe would be consistent with a small value for the bet coefficient - even setting aside cost consid-erations, (See the formulas on pp. 76 and 84 of this paper).

e) School Resources

Perhaps the single category of variables most susceptible to policy manipulation is that of schoolresources, Unfortunately, the variables used to measure school resources are very much like theII encyclopedias in the home" we discussed above. It is difficult to know whether, for example, librarybooks or laboratories are supposed to represent their own effects, per se, or whether they are supposedto represent a more extensive collection of items under the rubric of school facilities (or some otherconcept of school characteristics).

One can argue for either interpretation. On the reasonable assumption that libraries and laborff-tories are, Nould be, closely linked to an underlying specification of the usage of these facilities,

1, The possible misallocation of the effect is more likely if the student family characteristics or the school resources variablesare measured with considerable error. That a good deal of error is present in the measure of these variables has been strongly arguedby Bowles and Levin (malt, ) and by Rain and Hanushek

89

we could treat libraries and laboratories as proxies for the "usage conoopts, whioh in turn oan beplausibly linked to educational performanoe, Given this, the reader might further surmise that the twovariables must be standing solely for their own effects, for otherwise the authors would have includedthe other items.

If, on the other hand, it is naive to assume that faoilities present are faoilities used, and if it wouldhave been overly burdensome to inolude all relevant items in the survey, then we oan more readilyaooept the argument that the inoluded variables are meant to be representative of some different and/orlarger oolleotion. If so, we need to ask: a) what are these other variables, and b) what is the speolfi-eation (i. e. regression equation) by which they are linked to the other variables. This really breaks upinto two other questions: how aoourate is the representation (i. e. how strongly are they oorrelated),and what is the quantitative magnitude of the relation (1. e. what are the regression ooeffioients linkingthe full set of variables to the proxy variables') ?

The sort of questions we have boon posing serve to illustrate the analytioal weaknesses noted above.If the questions we have raised are overly demanding of the state of theoretioal knowledge about theeduoational prooesses, we oan only ask that this shaky base be made explioit. Perhaps researohers willbe led to work with a more simplified model that oan be well speoified and interpreted - better thisthan a oomplex model that defies interpretation,

1, The complexity of this specification need not be exaggetated, There are many decision contexts in which proxy variables

may represent a bundle of heterogeneous components, and it may not be worthwhile or expedient for the decWon-maker to distinguish

among the components to determine their separate measures of effectiveness, What is necessary, howeva, is some translation of a unitof the proxy variable into a unit of the larger bundle (along with, eventually, some measure of the costs of the larger bundle),

90

52

CONCLUSION

We are aware that a demand for theoretical rigour may be likened to a request for virtue. But wehope that the discussion in Parts III and IV has been sufficiently specific so that both the interpretationof the Coleman Report and the design of further studies will be improved.

Our criticism of the Co lomat, Report has been aimed at its methods and not at its substantive findings.The questions we have raised about the statistical and methodological techniques in the Report should beviewed as reinforcing the challenge to the "educational establishment" to provide evidence on the effec-tiveness of their programmes, especially compensatory educational programmes. Nor should any re-search into the determinants of educational achievement overlook the potential contribution that may stem,however indirectly, from the simple improvement in economic status of the student or his family or thefamilies of his fellow students.

1. The term was used by Daniel P. Moynihan in the context of his criticism that "educationists" - administntors, teachers,research personnel - have shirked their responsibilities to evaluate their performance and have attempted to use "technical" criticismof the Coleman Report as an excuse for continued inaction: (Daniel P. Moynihan, "Sources of Resistance to the Coleman Report",.larvard Education Revittaya Vol, 38, No, 1, Wintes, 1968, pp, 23-36),

91

Paper 3

EDUCATION AND INCOME:A STUDY OF CROSS-SECTIONS AND COHORTS

by

R. Hollister1

1, Mrs, Nancy Williamson and Paul Christianson assisted with research, and Harold Watts and Glen Cain provided guidance atseveral stages in the writing of this paper, I also benefited from discussions with Tom Ribich, Bernie Saffran, and Patrick Shima, Noneof these persons should be regarded in any way as responsible for any errors which may be found in this paper,

INTRODUCTION

The rapid growth in the application of economic analysis to the role of education in society duringthe past decade has been largely due to the development of the concept of human capital, a concept ad-mirably expounded by Schultzi Becker2 , Mincers and others. It may be argued that the wide accep-tance of this conceptual approach to educational problems owed no little to the fact that its advocateswere able to show its empirical relevance, for the difficulty in applying investment concepts to educationis that, since the return on education accrues during the whole working life of the recipient, empiricaltests of the human capital concept would normally require a lifetime of data gathering. This seemingbarrier to empirical testing was ingeniously circumvented by making use of cross-section profiles ofincomes as related to education and age, instead of the unavailable time-series. It was thus possible tobuttress the theoretical concepts with convincing empirical evidence.

Though time-series on the relationship between income, education and age are still scarce, thereare now enough successive cross-sections available to make possible at least a rough examination ofthe income patterns actually experienced over ten to twenty years by some cohorts in the United States.This paper is an attempt at such an examination.

It should be said at once that the comparability of the data over such long periods of time raisesvirtually insurmountable problems, and no great effort has been made here to ensure comparability.There must, therefore, be some doubt about the extent to which features in analysis reflect meaningfulsocial and economic forces at work; in fact, they may reflect no more than the incomparability of data.The discussion of data problems is relegated to the footnotes of the tables.

The issues dealt with here have been touched upon briefly by several authors; Beckert Millers ,

Ben-Poraths , Lansing and Sonquist7, Grilichess. Our analysis, however crude, goes somewhat furtherin that it deals with the specific issue of the differences between the cross-section profiles of age-edu-cation-income and the time-series experience of cohorts.

1. Schulte, Theodore W, "Investment in Human capital", American Economic Reviewt March, 1961.2, Becker, Gary S., Human Capitals A Theoretical and Empirical Analysis with Special Reference to Education, New Yors

National Bureau of Economic Research, 1964,3, Mincer, Jacob, "Investment in Human Capital and Personal Income Disvibution", Journal of Political Economy, August,

1958.4, Becker, Gary 5 op, cit.6. Miller, Herman P, , "Lifetime Income and Economic Growth", metagalgattoy, September, 1966.6, Ben-Porath, Yoram, "Lifetime Income and Economic Growth: Comment", ri_v_ii19.9.L.Q.iseae st, September, 1065,7, Lansing, John and Sonctuist, John, "A Cohort Analysis of Changes in the Distribution of Wealth", I, L. Soltow (ed,), Six

Pa ers t_s_2111111apis b./1ItiotI of Weft mil come, MisLin.laumg.ansLVIAt, No, 33, National Bureau of Economic Research.8, Griliches, Zvi, "Notes on the Role of Education in Production Functions and Growth Accounting", NBER Conference on

Research on Income and Wealth, Madison, Wisconsin, November, 1968,

95

55

THE DECISION ON EDUCATIONAL INVESTMENT

Before embarking on the empirical work, let us examine the framework within which it is to be set,and which is implicit in past studies of the rate of return on human capital using cross-section profilesof age-education-income. The following description, though distorted, has at least the merit of sim-plicity.

At a given point in his lifetime, say, at the age of 13 or 17, the individual is faced with a decision;he can leave school and enter the labour market, or he can continue his studies. In the latter case, hemust incur at least the cost of foregoing the wages he could have earned if he had left school, and per-haps that of expenses involved in further schooling. In terms of human capital theory, he must considerwhether investment in further education (through the cost incurred) will increase his future earnings tosuch an extent that the present value of these additional earnings exceeds the present value of returnshe could obtain by investing the same amount (i. e. the cost incurred) in some other way; in other words,whether the rate of return on further education exceeds the rate of return on alternative investmentsopen to him.

In order to make such a decision, the individual must be able to estimate, if only roughly, the in-crease in earnings which he may expect from additional years of education. It is suggested that suchan estimate can be arrived at by examining age-education-income profiles of people currently in thelabour force. For example, by taking the difference in typical (median or mean) earnings at given agesof tho: 3 with 12 years of education and those with 8 years, one can trace the likely age pattern of dif-ferences in earnings due to additional years of education. By applying the appropriate discount factorto the earnings differential at each age and totalling, one can determine the present value of increasedearnings likely to accrue during the individual's working life as a result of the additional education.However, one further adjustment needs to be made: earnings, in general, increase over time, and thismust be taken into account. Thus, a person with a given level of education might expect, by the timehe will have reached the age of, say, 50, to be earning more than the present 50-year-old with the samelevel of education. He will earn more as a result of the economic growth which will have taken place duringthe period in question. Thus, the cross-section earnings differential for each age due to additional edu-cation should be multiplied by a factor reflecting the compound annual rate of growth of earnings due toeconomic growth for the period in question. One can take the long-term rate of annual growth over therecent past as the expected rate of annual growth.

The way in which the expected income chart is constructed is illustrated in Diagram I. Aperson aged 20 in year n, with a level cif education rn, would observe the incomes in that same yearn of those older than himself, but with the same level of education m, (YCm .Cm in the diagram),

'45 SOand to these he would apply the value of the annual rate of long-term growth, g, compounded for thenumber of years it will take him to reach the given age. Thus, his expected income for age 30 wouldbe YErn = YCm (g)

10.30 30

567

Diagram I

Em=

Cm(g) 10Y30 Y30

E m

25

20 25 30

A

Now, supposing that an individual had in fact approached the decision with respect to education in

this fashion, how would his actual earnings experience have compared with the above prediction? Inother words, do the shifts in the cross-section profiles due to general economic growth operate in aneutral fashion (we draw this terminology from Ben-Porath I) with respect to age and educational levels?If these shifts are neutral, then the present value of additional years of education for different levels ofeducation, as actually experienced by age cohorts, will be in the same proportions as the estimates de-

rived from the cross-sections,

While this rather simple framework will be the basic one used in the examination of the data, thereare some more complex issues, often discussed in the cont of human capital theory, which should be

noted before we turn to the data, Basically, the posing of the educational investment decision problem

in terms of an income stream constructed from cross-section observations and multiplied by a compound

growth factor (by which income stream is usually reduced to an equivalent present value) is a convenientway of summarizing a more intricate set of forces relevant to the problem, In reality, one uses the in-ternal rate of return to express in a single value all the complex supply and demand factors which might

be expected to operate during the working life of the particular cohort of individuals whose education de-cisions are being made at a given time: a complex set of simultaneous supply and demand functions have

been reduced to a single present value or rate of return. In estimating an expected present value of an

income stream from cross-section data in the fashion described above, one avoids the identification of

particular supply and demand shifts which are likely to interact to produce an expected lifetime rate of

1. Den-Porath, Yoram, "Lifetime Income and Economic Growtht Comment", p, 8211 221.21.1t

A98yT

,

57

return on educational Investment, Broadly, the rates of return on present values of investment in edu-cation for a partioular ochort of individuals ooulb de affected by: shifts in relative demand for factorsof production resulting from changes in the composition of demand for final goodie or from technologicalchanges in production relationships; shifts in the relative supply of different types of educated labourdue to the educational investment in that cohort and In succeeding cohorts who will compete in the labourmarket during their working life; shifts in relative earnings associated with any asymmetrloal effectsof business cycle fluctuations on types of workers, With these complex interacting factors to be takeninto account, one oan appreciate the appeal of the simplification afforded by concentrating on.the cross-section present value or rate of return estimates. If, in fad, shifts in the oross-section age-education-income profiles due to economic growth are neutral, it is not necessary to attempt to unt angle thevarious forces at work, On the other hand, given this array of interacting forces, our traditional theorywoull lead us to be rather surprised (see Grilichesi) if such ieutral shifts were observed, No mechanismgenbeattag interactions suoh as to result in this type of neutral shift has yet been specified, In fact, thisis an Inherent limitation of the analysis which follows - we have not speoified a satisfactory model ofsupply and demand interactions to be tested against these data, The best we can do for the time beingis to use the simple framework outlined above to examine the extent of neutrality of shifts and to attemptto associate, in a rather haphazard fashion, any deviations from neutral shifts with some of the demand,supply, or oyelioal factors,

1, Witches, Zvi, "Notes on the Role of Education in Production Functions and Orowth Accoun:ing", 224.s22

II

THE 1939 TO 1959 EXPERIENCE

By combining the data from the censuses of 1940, 1950, and 1960, it is possible to get three "snap-shots" of twenty years of work experience for various age cohorts (problems of comparability of thevarious years are noted in notes 1-4 to Table I). It is therefore possible with these data to makethe sort of approximate comparison suggested earlier; twenty-year segments of the actual experienceof various cohorts can be compared with what would have been predicted if expected income had beenestimated on the basis of 1939 cross-section profiles of income by age and education level (with anexpected growth rate applied as outlined above). It will also be possible to check the neutrality of shiftbetween 1939 and 1949 and 1959 in the cross-section profiles.

In order to make this comparison, it is necessary to choose an estimate of the growth in incomesdue to general economic growth. Following Becker1 and (quoting) Cale , we note that: "The growthrate of the rise of real wages is basically composed of a) quality constant labor (due in large part to aslower growth in the supply of labor than the demand for labor) and b) the increase in the quality oflabor. We want to allow for the secular growth stemming from a)". Therefore, we take the rate ofgrowth of output per man-hour from 1925 to 1960 of 2. FV,"0. Now, in order to remove the portion of thisgrowth rate due to b) above, we reduce this rate by 25%. The resultant rate of secular growth in in-comes is 1-7/8% per annum.

The expected income path for the group of individuals of a given age and education in 1939, forexample those aged 203 Who completed 12 years of education, is formed by applying the value of thecompound growth rate to the 1939 median income of those with 12 years of education aged 30, 40, 50,etc. The compound growth rate is (1. 01875)9 = 1. 1819 for age 30, (1. 01875)9 = 1.4231 for age 40, etc.The resultant: expected income path as of 1939 is shown in Chart I. We can proceed in a similar fashionfor each age-education cohort, constructing an expected income path as of 1939 on the basis of the 1939cross-section and the expected secular growth rate.

The expected income paths thus constructed, we can make a comparison with the actual income pathover the period 1939-1959 by tracing the actual observed income of the cohort in the 1949 and 1959 cross-section data. For example, those aged 15-24 in 1939 were born in1915-1924, andforthis group's actualincome experience we t e the observed income of those aged 25-34 in 1949, and 35-44 in 1959. Thisjuxtaposition of the expected income path based on the 1939 cross-section and the actual income path for20 years provides the type of contrast discussed earlier. Comparisons of expected and actual incomepaths for various age cohorts are provided in Charts Ha-i,

1, Jacket, Gary S. Humatoraisilittid fried Anfd sisop.a,

2, Cain, Glen, "Ilenefit/Cost Estimates for job Corps", agatian2spir.124±2of Wisconsin, Madison, Wiaconsill, 1968, p, 42,

3, Charts and tables below the data are for 10-year age groupings, except for thegroup is 18-24, but subsequent groups are 10 years, e,g, 28-34, 38-44, etc,

101

Rafe nce tolksajlp2, p. 73,

, institute for Resetach on Poverty, University

first age group centred on 21, This initial

'rabic) I. PRESENT VALUES - EXPECTED AND ACTUAL1'2'3

CALCULATED AT A DISCOUNT RATE OF 6%

Table Ia,Cohort Ago Born 1896-1904, WhIte Maloe

(1) (2) (3) (4) (6) (3) 0)

PV

16+

, ...--1W4

16+

Docker

PV

12

PV

8 (1)-(3) (2)-(3) (3)-(4)

a) Actual 35,176, 38 35 716, 99 23,186, 64 17, 765. 44 11,989. 74 12,530. 35 5,421, 20

b) Expected .. , 33,109, 06 35,625. 67 23,813. 25 15,211. 26 9,295, 81 11,812, 42 8,601. 99

ActualRatio

11.110.1.0111=0.ffillNOIMMOONIMMIMII...IMMINall

1. 29 1. 06 0. 63---.Expected

Table lb.Cohort Age Born 1895-1904, Black Males

(1) (2) (3) (4) (5) (6) (q)

PV

16+

pv416+

Becker

PV

12

PV

8 (1)-(3) (2)-(3) (3)-(4)-a) Actual 16,1.52. 79 n. a. 12, 012. 76 10, 048. 69 4, 140. 03 n. a. 1,964. 07

b) Expected , 13,406, 36 n. a. 9 922. 64 8, 014. 68 3,483. 72 n. a. 1,907, 96

ActualRatio 1. 19 1. 03

.

Expected

Table IcCohort Age Born 1895-1904. Total Male Population

(1) (2) (3) (4) (5) (6) CO

PV

16+

pv4

16+

13e4ker

EN

12

PV

8 (1)-(8) (2)00) (3)-(4)

a) Actual 34, 180. 97 3:, 109. 75 22 526. 62 17,004. 75 11 654. 35 12,183. 13 30521. 87

b) Expected

ActualRatio

310898. 64 34,327. 69 23, 080. 85 14,516. 54 8 817.

1,

79

32

11 246.

1.

84

08

80564. 31

0. 64.

ExpectedWIUMMUOMIA

. 4.02

60

Table 1, (continued) PRESENT VALUES - EXPECTED AND ACTUAL1

'2 3

CALCULATED AT A DISCOUNT RATE OF 6%

Table Id,Cohort Age Born 1905-1914. White Males

(1) (2) (3) (4) (5) (6) (q)

PV

16+

PV4

16+

Becket

PV

12

PV

8 (1)-(3) (2)-(3) (3)(4)

a) Actual 63 187.57 63,508.02 41 603.75 32,753. 77 21,583. 82 21 904. 27 8 849.98

b) Expected , . . . 61, 720, 57 65,940. 43 44 176. 35 29 537. 45 17,544. 22 21 764. 08 14 638. 90

ActualRatio 1. 23 1. 01 0. 60,

Expected

Table RI,Cohort Age Born 1905-1914. Black Males

(1) (2) (3) (4) (5) (6) (7)

PV

16+

PO16+

Becker

PV

12

PV

8(1)-(3) (2)-(3) (3)-(4)

a) Actual 33,428. 02 n. a.i

25,104,157 20,632. 62 8,323. 45 n. a. 4,471. 95

b) Expected . .. . 26,953. 17 n. . 20,276. 61 16,214. 85 6,677. 16 n. a. 4,061.76

ActualRatio 1, 25 1. 10.

Expected

Table ILCohort Age Born 1905-1914. Total Male Population

(1) (2) (3) (4) (5) (6) (1)

PV

16+

PV4

16+

Becker

PV

12

PV

8 (1)-(3) (2)-(3) (3)-(4)

a) Actual 61,742, 47 62 055.41 40,744. 52 31,682, 15 20,997.95 21,310, 89 90062.37

b) Expected , , 60,280. 06 64,398, 57 43,123. 68 28,206. C8 17, 156, 38 210274, 89 14,916. 80

ActualRatio 1, 22 1, 00 0, 61

Expected

10361

Table I. (continued) PRESENT VALUES - EXPECTED AND ACTUAL1' 2 3

CALCULATED AT A DISCOUNT RATE OF 6%

Table Ig.Cohort Age Born 1915-1924, White Males

(1) (2) (3) (4) (5) (6) (7)

PV

16+

PV4

16+

Becker

PV

12

PV

8 (1)-(3) (2)-(3) (3)-(4)

a) Actual 82,566,95 82 566.95 63 875,02 49 304.28 18 691.93 18 691.93 14 570.74

b) Expected 80,368.18 84,044.34 58,727.44, 39,776.65 21,640.74 25,316.90 18,950.79

ActualRatio 0.86 0.74 0.77.

Expected

Table ih.Cohort Age Born 1915-1924. Black Males

(1) (2) (3) (4) (5) (6) (7)

PV

16+

PO16+

Becker

PV

12pv8 (1)-(3) (2)-(3) (3)-(4)

a) Actual 47,797.47 n. a. 41,969.65 33,365.43 5,827.82 n. a. 8,604.22

b) Expected 38 024.82 n. a. 29,594.73 23,718.30 8,070.09 n. a. 5,876.43

ActualRatio 0.72 1.46

Expected

Table Ii.Cohort Age Born 1915-1924. Total Male Population

(1) (2) (3) (4) (5) 0) (7)

PV PV4

PV PV

16+ 16+ 12 8 (1)-(3) (2)-(3) (3)-(4)Becker

a) Actual 81,219.66 81,219.66 62,696.21 47,683.41 18,523,45 18,533.45 15,012.80

b) Expected . 79,095.65 82, 714.09 67,595.27 38,082.19 21,500.38 25, 118.82 19,511 08

ActualRatio 0.86 0.73 O. 77

Expected

104

62

Notes to Table I:

1, All census data have been nonverted to constant 1957-1959 dollars.

2, 1940 census data have different educational groupings combining grades 7 and 8, whereas the 1950and 1960 censuses list grade 8 separately. The 1939 grades 7 and 8 data were considered as grade 8 only.3. The 1940 census reveals earnings, whereas the two later ones list income, Following the discussionin Becker' , we have increased all data by 10% to offset the rate of under-reporting of wages and salaries.No adjustment was made to data from 1950 and 1960 censuses because the under-reporting of earningsoffset the inclusion of other income, etc.

4. A further adjustment was made to the 16+ data from the 1940 cenous. Again following Becker' ,

the income figures for total male and white male population were increased to offset the effect of thecensus data not including respondents with "other income" exceeding fifty dollars, The percentage in-crease varied with age as follows:

Age 25-34: 2.7%Age 35-44: 6.9%Age 45-54: 8.6%Age 55-64: 6.3%

Both the adjusted an unadjusted 16+ data are used in this paper, No adjustment estimates for black maleswere available,

1, Becket,and 168, 2p,,

Gary S., ittDassakiait A Theoretical and Em _Weal Analysis with tecial_lefatenc_e_ to Ecincation, pp, 163

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A cursory glance at these charts indicates that the actual income paths deviated from those predictedon the basis of the 1939 cross-section and expected growth rate, Moreover, the deviations wvre differentfor different levels of education within ihe same age cohorts, and the pattern of relative deviations forvarious education levels differed among the different age cohorts, For example, for the total populationdata, the 1915-1924 age cohort with12 years of education, the actual income path wits somewhat below theexpected one, and for the 1895-1904 cohort with 12 years of education, the actual was also below theexpected.

We should say a word at this point about the use of the expected rate of growth adjustment, Naturally,the choice of the rate of growth is rather arbitrary; rationales could be provided for somewhat higheror somewhat lower rates of growth of quality-constant labour incomes, However, the arbitrary elementin the choice does not affect the conclusions, since the use of the common rate of growth is just a way ofproviding a common standard between levels of education and across cohorts; the differences in the char-acter of the deviations from the expected path would remain whatever the growth factor used.

Given that there are differences in the character of the deviations of the actual income path from theexpected path, it is still somewhat difficult to gather from the charts the significance of such deviations,To do so, let us retul.i to the simple decision situation outlined under Part I, There it was suggestedthat the present value of additional earnings due to more education might be estimated by taking the pres-ent value of the difference between cross-section levels of earnings - increased by a growth factor - andcomparing it with the present value of the cost of the additional education, This suggests that the signif-icance of deviations between expected and actual incomes might lie in the difference between the present1939 value of additional earnings due to education as derived from the expected paths, and the presentvalue as calculated from the actual paths. For example (see Table Ic), for white males in the 1905-1914cohort, the 1939 present value of income of those with 16+ years of education for the 20-year period upto 1959, as calculated from the expected path, is $72,379. For the same age cohort, the 1939 presentvalue of income for 12 years of education over the same period, as calculated from the expected (J. e,cross-section adjusted for growth) path, is $51,681. Thus the difference in present value of incomeassociated with the extra four years of education, as calculated from the expected paths, is $20,698,Now, the present value for the same cohort over the same period, calculated from actual experience,is $72,950 for 16+ and $48,776 for 12 years of education, giving a difference of $24,174. Thus, theactual difference in present value of income associated with the additional four years was 1.17 timesthe expected difference in present value, i.e, 17% higher for a period covering about half the workinglife. This difference seeils large enough to be regarded as significant,

When similar calculations of present values for 12 as compared to 8 years of educai ion for the samecohort are made, we find that the actual present value of the difference between 8 and 12 years is only, 64 times the expected present value, i. e, 36% less than expected, a significant difference in the oppomitedirection.

The present values for different cohorts calculated in a way similar to that just described are pres-ented in Tables la-i, Some further, but limited, comments on Table I may be in order, First, whenone uses the present values for 16+ calculated from paths which use the Becker correction of the 1939data (i.e. columns (2) and (6) in Tables Ia-i), the deviations of actual from expected present values aresmaller for the first two age cohorts (1895-1904 and 1905-1914); in fact, for Table Id and If they arenon-existent, However, for the third cohort (1916-1924) , the deviations of actual from expected are greaterwhen the Becker correction is used, Thus the oorreetion seems reasonable but does not remove thesignificance of deviations.

Second, the pattern of deviations for the present value of the additional years between 8 and 12 forwhite males (and total male population) seems consistent across cohorts, with the actual present valuebeing about .6 to 7 of the expected value, One might conclude from this that 1939 cross-section valuesfor those with 12 years of education were abnormally low, This conclusion would be consistent with thefinding foli the age cohort 1895..1904 of actual present value for 16+42 greater than one, but wouldconflict with the findings for the 16+-12 values for the other two cohorts,

116

74

Third, the most striking results are those with respect to the present value of the additional yearsfrom 12 to 16+, For the oldest cohort (white and total male), the actual exceeded the expected, for thenext cohort it equalled it, and for the youngest cohort it fell considerably short of it,

In most of the literature on the returns to investment in education, evidence is presented in termsof rates of return, It might, therefore, be of interest to give a rough indication of how deviations ofactual from expected values of the income stream might affect the rate of return, Appendix A presentsthe rationale for our calculation of the effects on rates of return, but few typical examples can be givenhere. If the rate of return based on the expected income stream had been 10%, an actual income st:eam

63 of the expected (as in column 7, Table Ia) would yield an actual rate of return of 3.9%; an actual/expected of 1. 19 (as in column 5, Table Ib) would yield an actual rate of return of 12. 9%, The graph inAppendix A can be used to translate other actual/evected figures into rates of return.

One must bear in mind that the estimates of actual incomes are approximative, since they are forten-year group cohorts and are mapped from only three observations for each actual income path. Justas there were significant differences between 1939 and 1949, there may have been significant differencesin opposite directions in the interim years. Since we do not have the information, it is difficult to tellhow seriously we may be misled by the filet that we must approximate from only three observations; wedo not know, for example, to what extent 1949 was typical. Since we have used medians, we would ex-pect the year-to-year fluctuations to be less than they would have been with means, but the only conclu-sion - a tentative one - must be that the limited data on hand suggest that there were significant deviationsof the actual income experience from what would have been expected on the basis of the simple decisionframework outlined in Part I. These deviations differ as between both levels of education and age cohorts,

As was suggested earlier, the question we have been asking is, to what extent have the shifts in thecross-t ection profiles of age-education-income due to general economic growth been neutzel 7 Sincethis concept of neutral shifts is central to the concept of using the cross-section income profiles asproxies for time-series (see Ben-Porathl ), let us pursue this point a bit further with respect to these9.0-ear data. We could define neutrality in either of two ways; a) we could look at the age-income pathtor any given level of education, and call a shift in the cross-section neutral if incomes for each age roseby approximately the same percentage, thus leaving the relative income at different ages about the same;b) we could look at the additional income due to education (e.g. 12 minus 8 years), and call a shift in thecross-section neutral if the differentials at each age rose by the same percentage. Obviously, b) is asomewhat more stringent criterion, but it is the one that seems appropriate to the simple decision frame-work we have been using.

Charts ma - Mc show the successive cross-sections. Table II gives, for successive cross-sections,the income differential associated with additional education at each age (in percentages). This table rep-resents a teat of A:eutrality of shifts in the sense defined in b). It shows clearly that the shifts were notapproximately neutral in this sense.

In Graphs Ia-lc, we plot the actual income at a given age and edonation level as a percentage ofwhat it would have been if the previous cross-section had shifted up neutrally in the a) sense at a rateequivalent to the 1-7/8% secular growth rate we have been using. These graphs present then a test ofneutrality in the a) sense for individual education levels, If the shifts for any eduea+ion level had beenneutral, the graph would have been approximately a straight line. These graphs show clearly that thetest of neutrality in the a) sense is not met for any of the education levels.

In the light of the results obtained by considering the cohort profiles, it is not surprising that thesuccessive cross-sections failed to meet the neutrality of shifts tests. Let us comment on these twodifferent ways of looking at the data, As suggested earlier, these are approximately equivalent ways ofposing the same question. If the Oifts had been neutral in the a) 'sense, the deviations of the actual

1, nen.Potath, Yoram, "Lifetime income and Economic Growths Comment", op, oft,

117

Table II, INCOME DUPPERENTIALS ASSOCIATED WITH ADDITIONAL EDUCATION

(in percentage)

1939 - 1949 1939 - 1959 1949 - 1959

AG E

A (Y 16+-Y ) A (Y 12-Y8) Art16+

. A (Y 12-Y8) A (Y10+

-Y12) A (Y12

-Y8

)

30 -57 - 6 13 16 163 24

40 29 -40 89 - 1 47 63

50 44 -33 129 -17 59 25

60 69 -30 181 . -23 66 11

(See note 4 - Table I)

A GE

1939 - 1949 1939 - 1959

(Y16+B

ecker -Y12) (Y16+

13ecker -Y12)

30

40

50

60

-61

4

10

36

2

53

75

126

from the expected cohort path would have been systematic for a given level of education across cohorts.If they had been neutral in the b) sense, the deviations in actual and expected paths and the differencesin present value would have been systematic across both cohorts and levels of education. However, wefeel that it is preferable to analyse the data in terms of the cohort profiles,. Looking at successivecross-sections as a whole can be somewhat misleading. We tend to forget, for example, that a presentvalue made up from a cross-section is a weighted (by the discount rate) sum of yearly incomes. Thepresent value actually experienced by a cohort is going to be lrawn from different components of suc-cessive cross-sections. Thl fact that these are different weighted sums of components means that it isnot easy to deduce from the cross-sections as a whole the actual experience of parcicular cohorts. Oncethe shifts in successive cross-sections deviate from nettrality in either sense, the relationship betweenthe cross-section profiles and the actual cohort experience becomes rather complex. One might conjec-ture that the propensity to concentrate on cross-section profiles as a whole in the past has tended toobscure some of the issues we are explwing here.

We can summarize this section by concluding that the twenty-year data indicate that the actualexperience of groups with different levels of education deviated significantly from what would have beenpredicted at the beginning of the period on the basis of the cross-section data available at that time.Had educational investment decisions been made according to the simple framework outlined under Part I,the actual returns on investment realized over the twenty years would have been substantially different

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from those expected, It should be stressed that this conclusion is based upon very soant data, and thusmust be oonsidered as a very tentative one.

Unfortunately, this finding does not advanoe us very much in the application of human capital theoryto educational investment decisions, It suggests that we should reject the rather simple decision frame-work outlined earlier, and seek to penetrate the greater complexity of inter-relationships alluled to atthe beginning of this paper,

128

III

THF 1956 TO 1966 EXPERIENCE

There is another body of data available which permits a somewhat more detailed, though stilllimited, exploration of the problems with which we are concerned here. A Current Population Reportof the United States Bureau of the Censusl gives age-education-income data for men in the United Statesfor selected years between 1956 and 1966. Since these data are provided for six years of this intervaland for individual age cohorts, more analysis is possible even though the period is shorter,

We concluded earber that, since the present values expected on the basis of the 1939 cross-sectiondiffered significantly from the actual present values as experienced by cohorts (cross-sections did notshift in a neutral fashion between 1939 and 1949 and 1959), an attempt should be made to analyse thepossible effect of supply changes, demand shifts and cyclical effects. We have not tried to construct anelaborate model which would permit us unequivocally to separate out these various factors. Our approachhere is much more eclectic, and, in any case, we shall take several different analytical tacks in tryingto obtain further insight into the relationships between age, education and income.

As a first step in the analysis of these data, we have repeated the earlier calculation of expectedand actual present values for various age cohorts and levels of education, We have used, for this pur-pose, the cross-section observations on mean income for each age and education level for 1956 andmultiplied these values by the appropriate compounded value of the growth rate (using the same valueas before) in order to construct an expected income path in a fashion similar to that illustrated inDiagram I;

The results of these calculations are reported in Tables IIIa-d. It should be noted that, with thesedata, it has been possible to trace expected and actual income paths for single-year age groups (insteadof the ten-year groups used before). Pour different age cohorts were selected for analysis; those whowere respectively 50, 40, 35, and 30 in 1956.

Once again we find sizeable deviations of the actual from the expected present values; the ratios ofactual to expected values range for the various cohorts from .86 to 1.02 for the 16+ - 12 years, andfrom .96 to 1. 20 for the 12 - 8 years. Again, using the method outlined in Appendix A, we see that, ifthe expected rate of return were 10%, then, for an actual/expected equal to 86, the actual rate of retunwould be 6.4%; and that for an actual/expected of 1.20, it would be 14. 5%,

It is again noteworthy that the experience of different age cohorts over the same ten years,1956-1966,is quite different; for each cohort, the extent to which the actual experience deviated from what wouldhave been predicted from the 1956 cross-section was somewhat different, Only two general patternsemerge: first, with the exception of the oldest cohort (1908), the ratio of actual to expected was on the

1, United States Bureau of the Census, Department of Commerce, "Annual Mean, Lifetime Income and Educational Attainment of Menin theUnited States for Selected Years 1986 to 1068", caantapligilabp.9a, Consumer Income, EMU p.80, No, 88, August 1968,

127

S4

Table III, PRESENT VALUES - EXPECTED AND ACTUAL1(IN CONSTANT 1957-1959 DOLLARS)

CALCULATED AT A DISCOUNT RATE OF 6% FOR THE TEN YEARS 1956-1966

Table Ma. Total Males, Cohort Age Born 1906

IMPPV16+

(2) (4)

2 )(1

(5)WM (2) - (3)12 - 8

a) Expeotecl 32,108. 02 18,792. 08 131246. 05 131316. 12 5 546. 03

b) Actual 31,886.34 19,012. 96 12,846. 02 121873. 38 6,166.94

ActualRatio 0. 968 1. 11

EXpeoted

.- _ NIP,MA'lame um). TOM iVia10101 cmnort ewe bowl nun

(1) (2) (3) (4) (8)

177---12 - 8

PV

16+

PV

12

PV

e)

16 - 12

a) Expected 36,960.32 21,200, 79 15,578. 66 15 759.53 5,622. 13

b) Actual 34,293. 40 20,687, 63 14,927. 06 13,605. 77 5460. 57

Actual0. 862 0. 99Ratio

Expected

Tame mo, Total males, conort Age porn ay...(1) (2) (3) (4) , (5)

PV

16+PV

12

PV

8

(1) - (2)16 - 12

(2) - (3)12 - 8

a) Expected 46,132. 17 28,691.51 21,367, 90 17,440.66 7,333.61

b) Actual 43,419.64 27,367.44 20,297, 95 161052, 20 7, 069. 49

Aotual0, 919 0. 96Ratio --

Expected

Table Md. Total Males Cohort A e Boni 1926

(1) (2) (3) (4) (5)

PV PV PV (1) - (2) (2) - (9)e 12 8 16 - 12 12 - 8

a) Expected 53 494. 80 37 112, 92 28, 020. 67 16 381. 88 9, 192, 25

b) Actual 520495.23 35,320, 51 26,475, 10 17$ 174. 72 10,845, 41

4,, ActualRat"' ItTicVd-o

1. 022 1, 2

1, Data for these calculations were drawn from "Annual Mean, Lifetime Income and Educational Attainment of Men in the United

States for Selected Years 1956 to 1966" current Pouglption Reports, Consumer Income, Series P-60 No, 56, 14th August, 1988,

Bureau of the Census, United States De artment of COMMeree.

128

S5

same side of one for both levels of education (16+ - 12 and 12 - 8); second, in every cohort, the ratioof actual to expected was higher for the 12 - 8 level of education than for the 16+ - 12 level. We shallnot comment further on these present value results, because they are primarily intended to establishthe fact that sizeable deviations of actual from expected present values were observed for this period;analysis of possible causes of such deviations is more readily carried out with different configurationsof the data.

The question of the relationship between cross-section income profiles and actual cohort incomeexperience has been studied by another author in a somewhat different context, H. Mil lei" examinedthe influence of economic growth on the incomes of various education cohorts over the period 1950 to1960. He compared the actual income change from 1950 to 1960 for each cohort, with the appropriateincome difference in the 1950 cross-section profile, and concluded: "When the age component of thetotal increase is taken into account, it appears that economic growth accounted for a 5.1% annual in-crease in income between ages 30 and 40; a 2. 0% inorease between ages 40 and 50; and 1.8% increasebetween ages 50 and 60. Since the latter element is not taken into account in traditional measures ofestimating lifetime income, it appears that its inclusion would add to the expected income gains ofyounger men and would therefore have an important bearing on the estimates of expected lifetime in-come, "

Ben-Porath2 suggested a correction to Miller's procedures which would eliminate the interactionbetween movement along the cross-section profile and a shift in that profile over time. After elimi-nating this interaction, Ben-Porath concludes; "The pure growth effect (eliminating the interaction) issomewhat higher in the age group 35-44 than in older age groups, but the decline where it exists is muchsmaller than reported by Miller, and in some cases there is actually an increase with age where Millershows a decline. It is also interesting to note that the group least affected by growth is the group 45-54and not the oldest group 55-64, "

Now these studies represent at least an attempt to get at some of the factors which might cause co-hort experience to deviate from cross-section profiles, The authors were suggesting that "economicgrowth" was distorting the cross-section profile. As was suggested earlier in this essay, a variety offactors could cause such non-neutral shifts in the income profile, We shall return later to a discussionof such factors but, first, let us compare the Miller and Ben-Porath results with those obtained fromthe data we have been using3.

For this purpose, we examine the data reported in Tables IVa-d. For the same age cohorts selectedfor analysis in Table III and for the same period1956-1966, we report inoolumn 2 of the tables, for eachof the years of observation, the ratio of the actual income of the education-age cohort to the expectedincome for that age-education class (constructed as described above), If we take the last entry in thatcolumn for each cohort education level, we have an indication of the experience of each group at the endof the ten-year period, This gives us a basis for comparison with the Miller and Ben-Porath data, whichalso covered a ten-year period (1950-1960). We find that for the 16+ level, the cohort with the highest ac-tual income relative to expected income is the oldest one, 1906 (who were 50 to 60 years of age duringthe period). Next was the yougest cohort, 1926, followed by the 1921 and, lastly, by the 1916 cohort,which had an actual income some 8% below its expected income, At first glance, this would seem roughlyin line with Ben-Porath,s conclusions, the youngest and the oldest cohorts doing better than those in be-tween. But these conclusions do not follow as one moves down to the lower levels of education: one ofthe middle age cohorts, 1916, does best in the actual/expected for level 12 and level 8, while the oldestcohort does worse at level 12 and the youngest cohort does worse at level 8,

I, Millet, Herman P "Lifetime Income and Economic Growth", gp,2, Den-Porath, Yoram, "Lifetime Income and Economic Growth: Comment", malt,3. Our method of constructing an expected income path and then checking for deviations from it is roughly equivalent to

Den-Porath's method of allowing for interactions,

129 86

Table IV, RELATION OP ACTUAL MEAN INCOMETO EXPECTED MEAN INCOME

FOR SELECTED AGE COHORTS FOR YEARS 1956-1966

(Same Data Base as Table III)

Table IVa. Table IVb.Cohort Age Born 1906 Cohort Age Born 1916

AGEACTUAL

AGEACTUAL

RATIORATIO -EXPECTO EXPECTED

16+ YEARS OF EDUCATION 16+ YEARS OF EDUCATION

50 1. 0000 4 0 1. 0000

52 . 9901 4 2 . ..... 9045

55 9448 45 . 9285

57 1. 0379 4 7 . 9017

58 9702 48 . 899 1

60 1. 0890 50 . 9558

12 YEARS OF EDUCATION 12 YEARS OP EDUCATION

50 1. 0000 40 1. 0000

52 1. 1786 42 . 9599

55 9475 45 . 9486

57 9626 47 . 9858

88 9536 48 . 9733

60 9614 50 1. 0132

8 YEARS OF EDUCATION 8 YEARS.OF EDUCATION

80 1. 0000 40 1. 0000

52 9142 42 . 9122

85 I ..... 1. 0145 45 . 9709

57 9558 4 7 . 9687

58 . 9538 48 . 9246

60 . 9919 50 . 995 1

130

67

Table IV. RELATION OF ACTUAL MEAN INCOMETO EXPECTED MEAN INCOME

FOR SELECTED AGE COHORTS FOR YEARS 1956-1966

(Same Data Base as Table III)

Table IVo. Table MI.Cohort Age Born 1921 Cohort Age Born 1926

AGE RAACTUAL

TIO AGEEXPECTED

16+ YEARS OF EDUCATION

35 1. 0000 30

37 9136 32

40 9471 35

42 9192 37

43 9225 38

45 9651 40

12 YEARS OF EDUCATION

35 1. 0000 30

37 8866 32

40 9374 35

42 9827 37

43 9599 38

45 1. 0044 40

8 YEARS OF EDUCATION

36 1. 0000 30

37 . 9084 32

40 . 9416 36

42 . 9582 37

43 , 9351 38

45 9908 40

131 tiis

ACTUALRATIO

EXPECTED

1 + YEARS OF EDUCATION

1. 0000

. 9981

. 9899

. 9391

. 9565

1. 0014

12 YEARS OF EDUCATION

1. 0000

. 8986

. 9349

. 9747

. 9552

. 9863

8 YEARS OF EDUCATION

1. 0000

. 9034

. 9244

. 9530

9459

9816

One might conclude that the differences between our results and those of Miller and Ben-Porath aredue to differences in the source of the data and the lack of complete overlap in the periods (1956-66 vs,1950-60), But the implications of these findings go further than that, Table V gives the relative ranksof age cohorts on the basis of the ratio reported in column 2 of Tables IVa-d, The first column showsthe ranks for the last year of observation, 1966, the results just described in the previous paragraphs,The next column shows the ranks for the middle year of the period, 1961.

Table V, RANKS OP COHORTS ACCORDINGTO ACTUAL INCOME/EXPECTED INCOME

YEAR 1966

a.

YEAR 1961

LEVEL 16+ LEVEL 16+

1. Cohort 1906 1, Cohort 19262, Cohort 1926 2, Cohort 19213. Cohort 1921 3. Cohort 19064. Cohort 19 16 4, Cohort 19 16

LEVEL 12 LEVEL 12

1. Cohort 19 16 1. Cohort 19162, Cohort 1921 2. Cohort 19063. Cohort 1926 3. Cohort 19214. Cohort 1906 4. Cohort 1926

LEVEL 8 LEVEL 8

1. Cohort 1916 1. Cohort 19062. Cohort 1906 2. Cohort 19163. Cohort 1921 3. Cohort 192 14. Cohort 1926 4. Cohort 1926

We can see.from this table that rankings not only differ according to the level of education, but alsochange considerably when a different terminal year is chosen as the point of comparison. This suggeststhat lumping shifts in the profile over a period into a broad term such as "the effect of economic growth"is misleading. The fact that the conclusions one might draw about such "effects" are likely to be verysensitive to the choice of the terminal year, suggests that the effects observed are due to somethingmore than a broad and steady force of the type one bnagines when the term "effects of economic growth"is used. The figures reported in column 2 of Tables IVa-d give the actual/expected income ratio foreach periods so that it is possible to see the extent to which the relative performance of each cohorteducation level group changed from year to year.

The judgment of the relative effects of the shifts over time on various cohorts is affected not onlyby the choice of the terminal year* but even more basically by the choice of the initial year. The latteris particularly important because it is that year's cross-section profile which provides the basis for theconstruction of the expected income path for all the cohorts, The importance of the choice of the baseyear is easily seen by looking at the cross-section profiles shown in Chart IV, where the 1958 cross-section is shown in relation to the 1956 cross-section, Table VI shows the actual/expected income ratiosfor 1966 which result when the expected income is constructed on the basis of the 1958 oross-seotion.

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_

65

A comparison of the results in Table VI with the corresponding figures in Table IV (or comparing rank-ings from Table VI with those reported in column (1) of Table V) shows that the choice of a differentbase year alters considerably the conclusions, For example, if we compare the 19 16 and 1926 cohortsat level 16+ usim the 1956 cross-section base (Table IV), we see that, at the end of the period, the 1916cohort has an aual/expected 5% worse than the 1926 cohort, whereas, if we use the 1958 cross-sectionbase(Table VI) ,the 19 16 cohort has an actual/expected 5% better. Similar differences in results appearacross education levels with a given cohort as well as across cohorts within a given education level,

ACTUALTable VI' EXPECTED

INCOME IN 1966 - USING 1958 CROSS-SECTION TO CONSTRUCTEXPECTED INCOME

(Same data base as Table III)

COHORT 1006 1916 1921 1926

Level 16+ 1, 0999 1, 0568 1. 0564 1, 0034

Level 12 0, 8 157 1. 0555 1, 1328 1, 0976

Level 8 1. 0850 1, 0909 1, 0907 1, 0866

One simple explanation of the differences between the results when using 19 56 or 1958 as a baseimmediately springs to mind: 1958 was a year of very high unemployment. In fact, there were ratherconsiderable fluctuations in the unemployment rate throughoutthe1956-1966period, andthese are reportedin Table VII. The differential effects of fluctuations in the level of economic activity on various age-education levels could have a lot to do with the variations in the experience of the various cohorts.

Table VII. UNEMPLOYMENT RATES 1966-1966

YEAR

1956 4. 1

1957 4. 3

1958 6. 8

1959 5. 5

1960 5. 5

196 1 6. 7

1962 5. 5

1963 5, 7

1964 5. 2

1965 4.5

1966 3. 8

134

Si

All this amounts to saying that deviations of actual from expected income of various cohorts cannotbe explained by the effeots of some broad, simple trends. To gain a better understanding of the forceswhich are af), ,,ting the lifetime incomes of various nohort education groups, 'et would seem necessaryto go beyond simple comparisons of trends a,td to formulate more complex analytical models. The nextpart describes some attempts in this direction. Let us say at onoe that we do not regard these attemptsas much of a advance - the formulation of the model is rather haphazard, and the limitations of the dataseriously restrict the validity of any inference. At best, they will serve as guideposts for further re-search.

135 92

lvA MULTI-FACTOR MODEL OF T1ME-SERIES

OF EDUCATION-INCOME RELATIONSHIPS

As mentioned earlier, rates of return on educational investment are determined by the interactionof several supply and demand effects, Such effects are likely to operate differentially over time onvarious age-education groups. We have already shown that the actual experience of particular cohortsvaried sizeably from what would havebeenprediotedfrom the use of a cross-section profile and a growthrate, and that attempts to characterize the effects of time shifts on the age-education-income profile onthe basis of particular "base year" and "end year" relationships are likely to fail. It would have beenconvenient for the analyst if either of these ways of dealing with the effects of shifts in demand and supplyrelationships had proved to be adequate; one of the attractions of the simple rate of return measure isthat it allows one to avoid this tangle of inter-relationships. Unfortunately, we cannot avoid dealingmore explicitly with the multiplicity of economic forces affecting education-income relationships.

The major obstacle to any efforts to deal more explicitly with the changing supply and demand effectshas been the lack of adequate data, Those used in the previous section are severely limited, but theyare better than any other which have been available until now, On that basis, we have attempted to con-struct a model which, while constrained by the data limitations, will at least be illustrative of the kindof effort which needs to be undertaken.

The data which we have at hand are:1) Mean income for males by age and education level for six years in the period 1956 to 1966

(See Table III for source).

2) The number of males by age and education level in the labour force in 1960. (Prom the UnitedStates Bureau of the Census 1/1000 sample data tape. )

3) National unemployment rates for the period 19564966.

Some preliminary results of our attempt to develop and estimate a model based on these did, 4nlyare reported in the following pages.

Appendix B develops in detail the rationale for the simultaneous supply and demand equation modelof the determination of income for a particular age and education group, Here we shall only discuss thereduced form equation of that system. (Of course, one may take a less structured view of this work andsimply look at the final single equation which is estimated as an ad hoc construct. Given the limitationsof the data and the resultant left out variables and simplified equation form, this would seem a reasonableview. The more elaborate structure in Appendix B is primarily intended to indicate directions furtherwork might take. )

The equation to be estimated is as follows;

Ya

Ya = A a + 13a e Sa + Ba Sr a + 13a Sra "+ + 13a T + e16,t 12,t 1 16

Ba,t 2 12,t 3 16,t 4 12 5 t 6 t t

where;

a mean annual income of males with 16 or more years of education, age a in year t,

a=

12,tmean annual income of males with 12 years of education, age a in year t,

Y

a number of males with 16 or more years of education in the labour force, age a in year t,

aS12

, t= number of males with 12 years of education in the labour force, age a in year t,

S16, t

24 the sum of the number of males with 16 or more years of education in the labour forcewith age a-2, a-1, a+1, a+2 in year t,

12,t =

Ut =

Tt =

et =

the sum of the number of males with 12 years of education in the labour force with agea-2, a-1, a+1, a+2 in year t,

the national unemployment rate in year t,

the number of years elapsed since 1956,

an error term.

The dep3ndent variable is, for a given age, the difference between the income of a male with 16 or moreyears of education and of one with 12 years of education. As noted above, this is the difference which hasusually been viewed as the resultant of the investment in the additional years of education. Note that there S'tk

would 1,e a different equation estimated for each age level, In this way, one would allow for a completelydifferent imp",4: of the various independent variables for each age level.

The four "S" independent variables are included to represent the relat!....e supplies of different typesof educated manpower. Including the 8 variables, made up of the sum of age groups two years on eitherside of the age group for the equation, represents a crude attempt to take into account the possibility ofskilled labour of approximately the same age as a competing source of skill supply, In general, thedifference in income between those with 16 and those with 12 years of education is taken to be influencedby the relative supply of these two groups in the same age bracket and of closely competing or comple-mentary groups in near age brackets.

The unemployment rate is used as a general variable to represent the level of economic activity.Its effect on the dependent variable would represent the differential impact of changes in the level ofeconomic activity on the two education level groups of a given age,

The time trend variable is, unfortunately, a catch-all variable for a number of factors, It couldrepresent trends in the composition of demand for final goods due to rising incomes, technologicaltrends in production relationships, and trends in the supplies of other factor inputs.

As stated above, there are only six years (within the period 1956-1966) for which we have obser-vations for the dependent variable, With seven coefficients to be estimated, we would have no degrees

135

94

of freedom left, Therefore, rather than estimate a separate equation for each age level, it was neces-sary to make some further assumptions in order to pool the data for all ages and conserve degrees offreedom. In order to do this, we assumed that the relationship for any given Bi across all the age

levels could be adequately approximated by a quadratic funotion. Thus, rather than estimate separateB

a, we could estimate a single equation for all the age levels of the following form:

Ya Ya A +B Sa + B aSa12,t a 1 16,t 2 16,t

Ea+ B 7S

16, t+ B

8aS

16, t

a+ 133a

2 Slept

EaB

9a2

S 16,t +

+3

U + B14

aUt + B

15a

2 Ut + B Tt

where a 32, 33, , 57.

a a a+ B4

S12, t

+ B5

aS12 , t

+ I36a2S12

, t

B SEa B aSEa

+ 13 a2 SEA10 12,t 11 12,t 12 12,t

+ 1317

aT + B18

a2T + et t t

Even with this formulation, the impact of the supply variables, the unemployment and time trendvariables oan vary by age, since those terms with a and a2 will differ for different age levels (ourassumption of a quadratic form relating coefficients across age levels does foroe these differential effectsto follow a certain degree of continuity).

This regression equation, quadratic with respect to age, was estimated in a stepwise fashion, InTable VIII, we report the results of the estimation where the stepwise procedure was out off at the pointat which multi-collinearity clearly began to appear (i, e. the corrected R2 began to fall with the additionof more variables).

The results of this regression are difficult to evaluate directly from the table and in order to facil-itate commentary we have, therefore, calculated the "net coefficients" for each independent variable atvarious age levels and charted them (Charts Va-e). The net coefficient for a given variable for a givenage is obtained by combining the regression coefficients (for example, for age 32, the net coefficient forUt is 4504. 3 + (32) (-199, 16) + (32)2(2. 0516) 232. 02).

We should like to remind the reader, as we proceed to comment on the regression results, thatthese estimates should be regarded as illustrative; these are only preliminary results and we intend toattempt further refinements in the estimation procedures.

Looking first at the net coefficients for UV the variable interpreted as reflecting the level of eco-

nomic activity, we find that it has a positive effect on the differential between college and high schoolincomes up to the age of about 38. Over this range, a lower level of business activity (higher lit) re-

duces high school graduates' incomes more than those of college graduates. After the age of 38 , the effecton high school graduates' incomes would seem to be less than that on college graduates' incomes. Ifthese estimates are even approximately correct, different age oohorts experiencing different levels ofbusiness activity at different points in the life oyole could thus have rather different lifetime earningspatterns. It might seem strange, at first, that for a substantial part of the age range the Ut net coef-

ficients are negative, since one normally thinks of those with less education being the first to be laid offduring periods of low economic activity. However, one must remember that these are measures ofmean incomes and that, while better-eduoated individuals may not a laid off, the rate of increase intheir incomes oan be considerably lessened and, therefore, their clAfferential gain over those with lowereducation decreased,

Turning to the net coefficients for Tt, one might compare these estimates with those of Miller and

Ben-Porath discussed above, The ooeffioients of this variable would, in a sense, reflect the "pure

139

95

Table VIII, RECIRESS1ON EQUATION FOR MULT1-FACTOR MODEL

Dependent Variableu Y1112,1

(N a 155)

INDIMNDBNTMIA01,11

COVPICIENT MATIO

A32

A33

A34

A35

A30

A37

A

A30

A40

A41

A42

A43

A44

A45

A46

A47

A48

A40

AGO

A51

A62

A83

A84

A85

A50

-0580. 0

-5700. 1

-4848. 8

-4023. 2

-3233. 7

-2485. 5

-1789, 3

-1143. 0

- 543. 8

0, 7

602, 2

939. 0

1209.8

1596. 0

1817. 2

1901, 5

2086. 3

2118. 0

2061, 9

1028, 7

1741, 2

147/, 1

1172. 5

836. 4

434, 2

^3. 230

-3. 030

-2. 825

-2. 580

-2. 305

-1, 970

-1. 595

-1. 142

- 010

. 008

, 800

1. 393

2. 039

2. 007

3. 064

3. 439

3, 703

3, 889

3. 969

4. 000

3, 092

1 865

3, 667

3, 104

2, 001

INDRPENDONT

VARIA01,2COOT Iclitt.rr T.RATIO

09496

. 00176

7. 9219

- , 20704

4604, 3

-199. 10

2, 0516

;a, Tt -2. 6684

a2, Tt 14160

R2 Corrected for D,P, .0034

* Stepwise procedure reached highest corrected R2before this variable entered

825

. 001

2. 162

- 2, 310

4. 464

- 4. 365

4, 007

-, 736

1. 425

economic growth effIct" they sought to isolate, The advantage of these estimates over those of Millerand Ben-Porath is, first, that they are less sensitive to the choice of beginning or ending periods -since they take into account each of the six years of obrervation withinthe ten-year period - and, second,that they are an even "purer" measure to the extent that the other variables in the model have taken intoaccount other effects. In spite of these advantages, one would be reluctant to call these coefficients "theeffects of economic growth", since they could be due to changes in other factor supplies, tastes, or tech-nology, as well as to the general growth in incomes, These estimates of time trend factors suggest thatthey cause the differential of the older groups to grow faster than that of the younger groups,

The coefficients of the supply variables,a

, SEa are the most difficult to interpret.16, t 12,t'

Appendix B provides a more detailed technical discussion about the expected signs of these coefficientswhen they are regarded as the coefficients of the reduced form of the demand and supply model spelledout there, We shall make only a few points here, and leave the rest of the discussion for the Appendix,

aThe first problem that one might note is that the S16, and S variables did not enter the equation

before the stepwise procedure reached the highest corrected R2, indicating that they were collinear withtheir respective Ea counterparts and that, therefore, their separate effects on the dependent variablecould not be estimated, Thus, rather than four supply factors, we end up with twe supply factors, 1. e.our attempt to separate out the effects of those with the same education level but slightly older or youngerdid not work. Our idea was that those groups might be either competitive with, or complementary to,the age groups concerned, but the data at hand do not allow us to isolate such group effects. The theo-retical meaning of these Ea groups, therefore, becomes rather cloudy and the results which emerge are

Eanot such as to help us very much in interpreting their meaning. Had the signs of the S been uniformly

aE 'negative and those of S 12, t

uniformly positive, we would have perhaps been able to interpret these fac-

tors broadly as representing two competitive supply sources. The fact that both are negative over awide range of ages and that they each have positive coefficients at slightly different points is confusing.Furthermore, it is hard to conceive of a theoretical explanation for the strong trends in these coefficientswith respect to age.

In general, the most disturbing result, from a theoretical point of view, is the fact that the coeffi-

cient of SEa

is negative over a wide age range. If this variable is thought of as representing the supply12,t

of those with 12 years .of education, one would expect the increase in that supply to lower Yan and toa '

raise 1'16,t, and thus produce a positive coefficient for the variable. The inadequacies of this model

are most clearly indicated by this result,

Once we have allowed simultaneously for the effects of the level of business activity, time trendsand supply factors, we have a set of coefficients, the Aa, which provides us with an age-income profile

for the differential associated with investment in education beyond the 12th year. We should note, firstof all, that the stepwise results indicate that the age variables alone can account for about 75% of thevariation in the dependent variable (the other variables add about 16 percentage points more to theexplained variation). There is no question but that age is an important variable affecting education-income relationships,

Chart Ve gives the age-income differential profile provided by the model estimates. This profilewas constructed by setting the unemployment and size variable at their mean values for the 1956-1966period and T at the mid-point value, 5, 5, andthen calculating the income differential values for eachage level.

Chart Ve also provides the profile drawn from the cross-section data for 1956, the base year.Note that neither profile allows for time trend shifts in relative incomes. The model profile is some-what higher at the outset, peaks earlier and drops off more sharply. From casual inspection, one

200

0

- 200

- 400

Chart V a

NET COEFFICIENTS FOR Ut

32 37 42

142

47

ES

52 57

350

300

250

200

150

100

50

0

Chart V b

NET COEFFICIENTS FOR Tt

Age 32 37 42

143

47

99

52 57

Chart VCia

NET COEFFICIENTS FOR S120

Age 32 37 42 47 52 57

+.200

-.200

- ,400

-.600

-300

-1,000

-1,200

Chart Vd

NET COEFFICIENTS FOR Si16,at

145

101

8 000

7 000

6000

5000

4 000

3000

2000

1 000

0

- 1 000

- 2 000

- 3000

- 4 000

- 5000

Chart Ve

AGE-1NCOME DIFFERENTIAL PROFILES

(Mean income males with 16 or more years of education

minus mean income males with 12 years of education)

/ 1 956 cross.sectlon

.00 aft.

.0 ft,imp MEP IMP WIMP mu,

" Pure age effect "

from model

_6 op

Age 32 34 36 38 40 42 44 46 48 50 52 54 56 58

146

might conclude that at reasonable discount rates the present value of the model profile might be some-what lower than that of the 1956 profile, However, it is important to recall that any cross-section datawill include the simultaneous interaction of a number of the factors whioh we have sought to represent inthis model, and thus one cannot decide, by looking at Chart Ve, whether the actual cross-section profileor the estimated profile comes closer to the type of measure which is basically implied by human capitaltheories.

There are still further implications for human capital theory which could be drawn from the partio-ular estimates provided by this model. However, since the model was presented primarily in order toillustrate an approach that seemed fruitful, we shall forego further &peculation about the meaning ofthose results.

10

SUMMARY AND CONCLUSIONS

The past decade has witnessed a tremendous growth in the literature devoted to the role of educationin the determination of incomes and in the growth of the economy. Studies on this subject have centredaround empirical estimates of income differences due to differences in the level of education. Theseestimates have been based almost exclusively on age-education-income profiles derived from cross-section data. The aim of this paper was to seek to answer a simple, but clearly very significant, em-pirical question: to what extent do the income differentials associated with education and observed at agiven point in time provide a good basis for predicting the actual income differentials which will be ex-perienced by cohort group over time?

It would have been very convenient if it had turned out that the cross-section data did provide asimple means of predicting the future differentials of the various cohorts. However, such a findingwould have seemed very strange from the point of view of traditional economic theory, since these dif-feren ials represent the relative prices of certain factors of production and the theory would lead us tobelieve that over time, as relative demand and supply forces shift, relative prices would also shift.

Though the data are very scarce, an attempt was made to compare income differentials for variouseducation groups in the United States as predicted from the cross-section data at the beginning of theperiod, and adjusted by a growth rate , with income differentials actually experienced by various cohortgroups over the period, The data used were those for a twenty-year period (for which there were threepoints of observation for ten-year age cohort groups) and for a ten-year period (for which the data werericher, having both 6 years of observation and sin0:10-year age cohort groups). The results showed thatthe cross-section data did not provide an adequat, ell,' simple basis for predicting time-series incomedifferentilds. For both the twenty-year period the ten-year period, the actual income differentialsof various cohorts differed sizeably from what would have been predicted from the cross-section data.For example, illustrative calculations suggest that actual rates of return on investment in education ofsome cohorts might have been as much as 6 percentage points below those predicted from the cross-section data in some cases (e. g, if the expected rate of return was 10%, the actual rate of return wouldbe only 4%), and as much as 4.5 percentage points above what would have been predicted for other cohorts.There was no clear pattern to these differences; some cohorts exceeded, some fell short of predictedvalues.

It might have been hoped that these differences merely reflected some sort of simple long-termtrend associated with the process of economic growth. In fact, there have been one or two commentsin the literature suggesting that this was so. If this had been the case, it would still have been possibleto utilize the cross-section data for prediction purpoees by adding some simple trend adjustments.However, it has been shown in this paper that simple long-term trends which might be labelled "effectsof economic growth" are not an adequate explanation of the changes in income differentials over time;the effects of "trends" in income differehaals are shown to vary according to the choice of base yearsand final years over which to measure such trends. Thus, the hope that simple trend corrections of thecross-section data will provide an adequate basis for prediction must be abandoned.

149

104

The easier routes having proved fruitless, an attempt was made to formulate more complex modelsof the determinants of income differentials of various education groups over time. The idea (hat, overtime, many economic and social factors are likely to interact in determining rates of return on invest-ment in education has certainly been advanced by many of the student! Amu capital theory, but littlehas been clone empirically to isolate such factors and to estimate ir effects. Probably (he primaryreason for the absence of this sort of empirical investigation has boon the lack of adequate time-seriesinformation on many of the relevant variables, most particularly age-oducation-income data.

Data limitations remain a serious obstacle, but the last part of this paper describes a prolhninaryattempt to utilize some ten-year data for the United States to estimate a crude multi-faotor model of thedetermination of age-education-ineome relationships. The results of this attempt are described not be-cause they are conclusive, but, primarily, because they serve to illustrate the kind of investigationwhich might have to be undertaken if a deeper understanding of age-education-income relationships is tobe achieved. The model described allows for the simultaneous effects on income differences of variablestaken to represent age, the level of business activity, supplies of various types of educated manpower,and time trend factors.

The following conclusions can be drawn from the results;

a) The impact of the various forces on income differentials varies substantially with age,

b) Variations in the level of business activity have substantial effects on income differentials,these effects being different at different ages (since most cross-section studies in the UnitedStates have been drawn from censuses taken at periods of relatively high unemployment, thiscould have had serious effects on returns estimates).

c) Time trend factors seem to be increasing differentials, faster at the older age levels,

d) Variables which were meant to reflect the relative supplies of educated manpower did not op-erate very well in the model, suggesting that the specification of such variables was inadequate.

It must be recalled that the model described is crude, the results preliminary, and the data limi-tations severe; but the results seem to indicate that this type of approach to the empirical problem isworthy of further investigation.

It might be useful to comment on how the results presented in this paper reflect on the long-standingcontroversy over the relative merits of the manpower planning approach and the rate of return approachto educational planning (see for example Blaug1). Earlier, this controversy was largely carried out interms of the theoretical strengths and weaknesses of each approach. More recently, empirical evidencehas been presented which substantiates the weaknesses of the manpower planning approach proceduresutilized to date (see, for example, Bowles2, Chapter V, Psacharopoulos3 and Hollister4). Since therate of return approach to educational planning has made use of cross-secLon data as the basis forestimates of returns, it must be concluded, in the light of our results, that empirical evidence substan-tiates the weaknesses of that approach too. In the case of both approaches, the wealoiesses are the re-sult of simplifications aimed at obtaining in the short term empirical results of some operational useful-ness. In the light of our results and those of the studies which illustrate the weaknesses of the manpowerplanning approach, it seems clear that an adequate understanding of the relationship between education andincome differentiath and of the role of education in economic growth will only be reached by more inten-sive investigations along the lines suggested by the multi-factor model described in this paper. It has

1, 81aug, Mark, "Approaches to Educational Planning", gconomle Journal, June, 1967,2, Bowles, Samuel, Planning Educational Systems for Economic Growth, Cambridget Harvard University Press 1969,

Chapter V,3, Psacharopoulcs, George, "Estimating Shadow Rates of Return to investment in Education", ournal of Hun, An Resources,

Winter 1970,4, Hollister, Robinson 0,1 Alichnical Evaluation of the First §ansf the Mediterranean Reliatlitilillea. OECD, 1967,

lbs

been useful, perhaps, to ignore these complications during the last decade, while the basic elements ofhuman capital theory were being developed. If, however, this type of work is seriously to influencefuture policy, these simplified procedures will no longer be adequate, Economists have long recognizedthat the theory of capital is a complex subject, and a difficult one to translate into operational terms,The results reported in this paper suggest that human capital theory shares these characteristics,

Appendix A

A CRUDE METHOD FOR TRANSLATING RATIOS OF PRESENT VALUESINTO RATIOS OF INTERNAL RATES OF RETURN

It may be recalled that in the application of capital theory to investment in eduoation, either of twoapproaches (equivalent, except in a few unusual cases) is used;

a) the income differential stream attributed to the eduoational investment is reduced to a presentvalue by discounting by the appropriate social (or private) discount rate; total costs (direct andforegone earnings) are calculated and similarly discounted, and the ratio of the present value ofincome differentials and the present value of costs is used as the measure of the value of the in-vestment - as compared to benefit-cost ratios i'or other investments;

b) the internal rate of return is calculated by finding the rate of discount which will cause the presentvalue of the stream of income differentials just to equal the present value of the total costs,

Tables I and II in the text show the ratio of present values of income differential streams (discountedat 6%), Since some people prefer to discuss these matters in terms of internal rates of return, we needa simple inethod to translate these ratios into differences of internal rates of return, For example, ifthe present value of the actual income differential stream is less than that of the expected stream, theactual internal rate of return will be smaller than the expected one, In general, it is not possible tomake a simple translation from ratios of present values to ratios of internal rates of return, since therelationship between the two depends on the specific time-shape of each of the income differential profiles,However, if we make the rather strong assumption that the actual and expected differential streams differonly by a constant of proportionality, it is possible to provide some illustrative relationships betweenthe two ratios.

For the purposes of the illustrative calculations, actual total costs are not need% d, The problem isevaluated from the point in time at which the investor has just completed his educatioi, and is about toenter the labour market, Thus the present value of total costs is a fixed sum. It is then asstmted thatthe expected income differential stream was Catch that a discount rate of 10% was just sufficient to reducethe present value of the stream of equality with the given total costs, I, e, the expected internal rate ofreturn was 10%. The problem then is to find the rate of discount which would just reduce the actual in-come differential stream to the given total cost value, i. e, to find the actual internal rate of return,To do so, we proceed as follows:

1, Assume the expected internal rate of return was 10%, 1. e,

a) P, V,e

= Ye/ (1 + 10)1 TCn, 10

where Ye = expected income differential in year i attributed to additional education,

183i t

TC total costs of the educational investment up to year 0,

PV = present value of the n year expected income differential stream discountedn,at 10%.

b) PVa

=n,10

Y1/

(1 . 10)

where Ya

= actual income differential in year i attributed to additional years of education,

aPV = present value of the n year actual income differentia stream discounted atn,

10%,

2, The annualized equivalents of these two present values are:

PVe = S

eA

n, 10 11,10

aPVn,

10= S

aAn,

10

where Se, Sa= the annual amount equivalents,

An,10 = the present value of 1 dollar per year annuity for n years at a 10% discountrate.

PN'n,10

Se

An,10

Se

aPVn,

10Sa

An,10

Sa

This is the point at which the assumption of proportionality of the expected and actual income

streams is important, for, if Yai = Yei (p) for all i (p being the constant of proportionality), the

ratio of PVe

and PVa will be the same at any discount rate, Thus the ratios of the present

values which are in Tables I and III in the text aro at a 6% discount rate but,

PVn,6 seAn16 Se PV1111.0

aPNin,6 S

aAn16 S a PVti,10

3, It has been assumed that

TC = PVn,10

103184

The figure sought is that discount rate, x, which would cause:

aPVn,

x= TC

Substituting the annualized values, the result is:

SaA = TC = S

eAn,10 orn,X

seAn,

x sa An,10

4, has been shown equivalent to the ratio expected present value/actual present value which

appears in Tables I and III. An,10

is drawn from a total of present values of 1 per annum at

compound interest. Multiplying the An, from the table by , the value of An,x

is obtainedsa

and the value of x is determined from the same present value annuity table. For example:

PVe06/PV 20a 10

= 1/.8

A2010 = 8.5136,

A20

1/.8 (8.5136) = 10.6419 which by reference to the table yields x = 069.,x

5. The results of this translation from the ratio of present values into internal rates of return,made on the assumption that the expected internal rate of return was 10%, are provided inChart A. The several assumptions made in this translation make it only a very rough meansof approximation of relationships between relative present value and internal rates of return.The results should, therefore, be regarded as very approximate.

i039153 ;.

Rate of return.16 "

.14

.12

.10

,08

.06

.04

.02

Chart A

Actual present value

Expected present value

1,20 1.10 1.0 .95 .85 .80 .75 .70 .60 .50

156

Ito

Appendix B

A SUPPLY AND DEMAND EQUATION MODEL FOR AGE EDUCATION-INCOME RELATIONSHIPS AND SOME EVALUATION OF ITS COEFFICIENTS

1, Define

DA = demand in year t foi labour age A with 16 years or more of education,16,t

AP16 , t

= price (yearly income) in year t for labour age A with 16 years or more education,

AP

12, t= price (yearly income) in year t for labour age A with 12 years of education,

EAP = average (weighted) price (yearly income) in year t for labour age A-1, A-2, A+1,16,t A+2 (=EA) with 16 years or more of education,

12 t average (weighted) price (yearly income) in year t for labour age A-1, A-2, A+1,,

A+2 (= EA) with 12 years of education,

Ut unemployment rate in year t,

Tt = years elapsed since 1956 in year t,

eit error term for equation i,

Then assuming a linear demand function for labour age A with 16 years or more of education;

Define:

DA6

= demand in year t for labour age A with 16 years or more education,1, tA

D12, t

= demand in year t for labour age A with 12 years education,

DEA16

= demand in year in year t for labour age A-1 A-2, A+1, A4.2 with 16 years or more,t education,

DEA demand in year t for labour age A-1, A-2, A+1, A+2 with 12 years education.12,t

Then the demand functions for such labour are:

A A AE

A EA A012, t

= a21

+ b21

P + b22

P + b P + b P + b16,t 12,t 23 16,t 24 12,t 25

Ut + b26

Tt + e2t

DEAA

= a + b A + b PA PEA EA+16,t 31 31

P 16,t 32 12,t+ b

33+ b

12,t 34P b

12,t 35

Ut + b36

Tt + e3t

D arA A

= + PA PA EA EA12,t 41

b41

+ b16,t 42+ b

12,t 43P + b

16,t 44P + b12,t 45

Ut + b46

Tt + e4t

Define:

AS

16, t= supply in year t of labourers age A with 16 or more years of education,

AS

12, t= supply in year t of labourers age A with 12 years of education,

EAS = supply in year t of labourers age A-1, A-2, A+1, A+2 with 16 years of education,16,t

EAS = supply in year t of labourers age A-1, A-2, A+1, A+2 with 12 years of education.12,t

It is assumed that supply of labour is taken as constant for any year, so that the supply functionsare simply:

A A'S

16, t= S 16,t

A A'12 , t

EA=

SEA'S

16,t 16,t

sEA sEA'12,t 12,t

where S' is the fixed supply in a given year.

With these eight supply and demand equations for each age group, and the equilibrium conditionsfor all types of labour where D S, it is possible to calculate the price of each type of skilledlabour for each age group.

158

112

The price equations are:

A AP16, t

dA SA + ciA

SA + dA SEA + dA SEA + CIA1 11 16,t 12 12,t 13 16,t 12 15,t

U+da T+Wt 16 t

A= CA + d SA + d A

SA + dA SEA + d AsE

A+ d

A12,t 2 21 16,t 22 12,t 23 16,t 24 12,t 25

AUt d

26Tt W

2t

A ASubtracting' P12, from P16, tt

A A A _EAP 16,t - AP 12,t = C + D

AS

A+ DA SA + DA SEA + D s + DA DA

1 16,t2 12,t 3 16,t 4U + T5t t

+ Wt

This is the basic formulation of the text equation on page 138, except that notation is shifted by sub-stituting P for Y, A for C, B for D, e for W and a for A.

A2. If the further assumptions are made that coefficients of the reduced form PA - P 12,t are16,trelated among the various A by the following equations, quadratic in A.

DA D1 + D2A + D3 A21

AD

2= D4 + D5A + D6 A2

AD

3= D7 + D8A + D9 A2

AD4 = D10 + D11A + D12 A2

AD = D13 4. D14A + 015 A2

AD

5= D16 + D17A + D

18A2

then the 26 PA - PA12,t equations for A = 32, , 57 can be reduced to the single equation:16,t

6,tA A A

PA - 12,tPA CA

+ D SA + D2

A SA16

+ D3

A3

S 16,t + D4

S 12,t + D5

A S 12,t1 1 16,t ,t_EA

+ 1D6 A2 SA2

+ D7

SEA + D8

A SEA + D9

A2 SEA + D1,t 16,t 16,t 16,t 10 12,t

+ D11

S 12 t +I)12

A2 SEA +I)13

Ut

+D14

AU +D A2 t, t 15

+ D16 Tt + D 17A Tt + D18 A2 Tt + Wt,

159

113

which is the formulation of the text equation on page 1.39, except that the notation is shifted bysubstituting P for Y, A for C, B for D, e for W, and a for A. This is the equation which wasestimated.

3. It is useful to try to deduce the expected sign of the reduced form coefficients using some as-sumptions about the sign and relative size of the coefficients of the structural demand equations.

a) Although the basic model is formulated with four supply factors, SA SA SEA16,t' 12,t' 16,t'sE

A it is useful, first, to try to evaluate the sign of reduced form coefficients for a12,t'

model with only two supply factors. This step is useful because the reduced form coeffi-cients are easier to manipulate with just two supply factors, but, more important, be-

EAcause in the actual estimation process SA

6and SA

12, were so collinear with S and sE A1,t ,t 16,t 12,t

that they would not be distinguished statistically. Thus, in the estimation sense, the modelwas reduced to a two supply factor model. The equations of the two supply factor modelwould be:

DA = aA+b PA

11 16, t+b PA

12 12, t+b U +b T +et

16,t 1 13 t 14 t 1

DA aA+b PA +b PA +b U +b T12,t = 2 21 16,t 22 12,t 23 t 24 t

+ e2

SA = SA

116,t 6, t

AS = SA'

12,t 12,t

The reduced form of the equations PA16,

tminus the reduced form equation for PA12,t

would be:

PA6,t - PA = CA + DA SA16

+ DA SA12t + DA U + DA Tt

+ W1 12,t 1 ,t 2 , 3 t 4 t

Athe coefficients to be evaluated being DA and D2

1

From the solution of the structural equations, the expressions for the coefficients areobtained:

b12DA = () (

2 b22

,b21 1

`1322/ 132 -b12 b21)

b11

2b21

b22

12

12b

21b

11 2- b

12 21b

11

bll

2

b) Recalling that the bij are the own-price response of demand (when i = j) and the cross-price

response of demand (when i j), the following assumptions would seem reasonable for thenormal case:

160

11.4

assume:

b11"

b22

<0" b12

b21

> 0" lb11

1> lb12

1" lb22

1 >1b21

1

The denominators of the terms in both equations are positive, since:

b11

b22

> 0' b12

b2 1

>0 and b1 1

b22

> b12

b21'

Looking first at DA"

b22

is negative and greater than the positive numerator b2 1"

so the1

Asign of D1 is negative, For DA the numerator (-1311) is positive and greater than the2

negative numerator (-b12), so the sign of DA is positive,2

Thus, if the two supply factor is the relevant one (since the other two factors are statis-Atically inseparable), the expectation should be that the sign of the D coefficient is negative

and the sign of the DA is positive. This expectation is not satisfied for all ages (values of2

A) in the estimated model.

4. When the coefficients of the reduced form of the four supply factor model are subject to anattempt at a similar evaluation, the result is not so clear. The reduced form coefficient is aquite complex combination of sums and cross-products of the structural bij and does not yield,

with manipulation, a form which can be clearly evaluated in a fashion similar to the two factorsupply model. The signs of the coefficient seem to depend on the relative size as well as thesign of the bij, and simple assumptions, such as those used in 3 b), do not yield an unambiguous

outcome. It does not seem possible, therefore, to develop clear expectations about the signsA Aof the Di, , Dn in the four supply factor case, Thus, if the correct model is a four supply

factor model, positive or negative signs of the supply coefficients would not lead to an immediateconcern about misspecifieation of the model.

161

115

Paper 4

PATTERNS OF RATES OF RETURN TO INVESTMENT IN EDUCATION:SOME INTERNATIONAL COMPARISONS

by

W. Lee Hansen'

1, W. Lee Hansen is Professor of Economics and Educational Policy Studies, University of Wisconsin, and Research Associate,

Institute for Research on Poverty. The research reported here was supported by funds granted to the Institute for Research on Poverty at

the University of Wisconsin by the Office of Economic Opportunity, pursuant to the provisions of the Economic Opportunity Act of 1964.

The research assistance of Padl Christensen dnd the comments of Mbimon Hollister and Louis EmrneriJ are pratefully

acknowledged.The financial support of the Ford Foundation is gratefully acknowledged,

116

GENERAL INTRODUCTION

The paper reviews the numerous studies for different countries which report rates of return to in-vestment in different levels and amounts of schooling. An effort is made to assess their comparability,to determine whether any empirical generalizations can be derived, to explore the general nature of thepolicy conclusions drawn, and to suggest some of the directions that future work on rate of return pat-terns should take, A special effort, though not a very successful one, is made to relate various oduca-tional distribution data to the observed rate of return patterns.

117163

INTRODUCTION

A dominant theme in the American work on the economics of education is the rate of return approachto decisions about human resource allocation. This stands in marked contrast to much of the Europeanwork and to one stream of American work which reflects a planning approaoh. Not only do these two ap-proaches differ, but they also indicate in their purest forms rather divergent ways of viewing the labourmarket and the education-training market. The purpose of this paper is not to fan the flames of contro-versy by arguing the superiority of one approach over the other - more likely they complement eachother, as has been suggested by Blaue, Instead, this paper reviews the now numerous rate of returnstudies, to determine whether any empirical generalizations can be derived from them, to explore thegeneral nature of the policy conclusions which have been drawn from them, and to suggest the directionsthat future work in this area should take. In doing so, a special effort has been made to examine thee'dsthig educational distribution data - educational attainment, school enrolment patterns, and the like- to help explain the observed rate of return patterns. This effort, while only moderately successful,did produce a clearer idea of what other types of education distribution data are needed and what otheranalyses are essential to interpreting the varying patterns in the rates of return to educational invest-ment in different countries, Hence, this paper represents an initial foray into an uncharted area andthus is far from being a definitive piece of work.

THE RATE OF RETURN APPROACH

The rate of return approach, developed largely by Becker° 3 and Schulte' f5 , characterizes muchof the initial work on the economics of human investment in the United States during the late 1950's andearly 1960's. In essence, this approach recognizes that human investments in education involve costoutlays - to the individual and to society - which are expected to produce a stream of benefits, largelyin the form of higher earnings over the working life of those who acquire schooling. The internal rateof return summarizes in a convenient way the relationship between the costs which are concentratedover a short span of years and the benefits which accrue over a much longer and more distant timehorizon. The mechanics of the caloulations and the definitions of costs and benefits ordinarily employed,as well as important qualifications to rate of return studies, need not be reviewed here (Becker*, Hansene).

1, Blaug, M. , "Apptoache.. to Educational Planning", fsamigIglawg, June 1967, pp, 262-288,2, Becker, G,S "Underitivestment in College Education", AzialagalunguiLkylea, May 1960, pp, 346-354,3, Becket, G.S., pitman Princeton: Princeton University Press, 1964,

4, Schultz, T, W. , "Education and Economic Growth", in N,B, Henry ed $ooiAl rces.....

Chicago: University of Chicago Press, 1901, Part 11, pp, 4648,5, Schultz, T,W "rho Rate of Return in Allocating Investment Resources to Education", tlatagLusimatgatoi, Summer

1967, pp, N3-310,0, Hansen, W,L "Comment Harberger's Estimate of Rate of Return to Investment in Education in India", Mimeographed,

August 7, 1963,

167

Us

The usefulness of the rate of return approach to questions about human resource allocation has beenstreEsed by Schultz', Johnson3. and So low.' among others4, All of them emphasize the need for abroad ct)ncept of capital, one that embraces the major stocks of productive resources - physical andhuman alike, They also maintain that only by knowing the relative returns to these differing inputs caneffective decisions be made about the whole gamut of activities and progTammes involving education andtraining

While a major concern of the United States has been that of achieving greater economic efficiency,in the narrower sense, that is, making the best use of existing resource inputs, many nations are con-cerned with finding efficient ways to greatly and quickly augment the quantity and quality of their humanresource inputs, The need for a better educated and trained labour force has long been apparent. But inthe 1050's this need was dramatized by the studies of Fabrioant5 and Kendrick° who discovered the "re-sklual" - the large Increment to economic growth left unexplained by conventional labour and physicalcapital inputs - and by Denison'7 whose pathbreaking work attributed a good part of the residual to edu-cation and the production of new knowledge. As a consequence of these efforts, there appears to be agrowing convergence of interest in rate of return analyses and oontribution-to-growth studies in theless-developed countries (Gounden8,9; Williamson1)3 ,1"). Contribution-to-growth studies indicate therole of education in accounting for past economic growth and are also suggestive of the effects on fu4ireeconomic growth. Hate of return studies complement growth studies through their focus on the variouslevels of schooling. Thus, they show more precisely the relationship between the benefits and costs ofdifferent types and levels of schooling, in the recent past and presumably in the near future as well.

As yet we know little about the relationship, if nny, between the rates of return to the various levelsof schooling and other characteristics of the economy and society - its level and rate of development, thelevel and distribution of educational attainment, the current flow of graduates from the educational sys-tem, and the like, Carnoyll has speculated on some of these relationships, and Harbison and Myers11have attempted some analyses along these lines, though without reference to rates of return to schooling.

1. Schultz, T. W., "The Rate of Return in Allocating Investment Resources to Education", ,Iournal of Human Resources, Summer136'i, pp, 293-310.

2. Johnson, IL G. , "Comment" in The Residual Factor in Economic Growth, Organisation for Economic Cooperation andDeve:opment, Paris 1964, pp, 219-227,

3, Solow, R. M ggpjtal Theory and the Rate of Return, Amsterdam: Rand McNally, 1963,4. The criticisms of the rate of return approach are numerous and no attempt is made here to coer that well-explored territory;

for a good review of the entire discussion, sees Pandit, 11,N., Erltagyny_of u...vestmenz Concej,tuat lEitawarisjTechniques and Maier Findings, New Delhi: National Institute of Education, 1969.

5, Fabricant, S. Basic Facts on Productitty Change, New York: National Bureau of Economic Research, 1059,6. Kendrick, LW., productivity Change in the U. S. , Princeton: Princeton University Press, 1981,7. Denison, E. E. , 1111._Sources of Growth in the U, S. and the Alternatives 13efore.Us, Washington, D,C,: Committee for

Economic Development, 1962,8, Gounden, A, M.N., "Education and Economic Development", unpublished Ph, D, dissertation, Karukshetra University, India,

1965,

9. Gounclen, A. M.N., "Investment in Education in India", Jornal of Human Resources, Summer 1967, pp. 347-388,10. Williamson, J.G., "Economic Growth in the Philippines: 1947-1965: The Role of Traditional Inputs, Education, and

Technical Change", Institute of Economic Development and Research, School of Economics, Univ:irsity of the Philippines, Discussioqanff_NOL.S11:110 September 12, 1907.

11. Williamson, J, G., and DeVorett, DJ., "Education as an Asset in the Philippine Economy", in M.D. Conception, edPhilippinGPopuiation in the Seventies, Manila: Community Publishers, Inc, , 1969, pp, 133-168,

12. Carney, M., "Rates of Return to Schooling in Latin America", journfil an Resources, Summer 1967, pp. 359-374,

13. Harbison, F. and Myers, C,A Education Iviannemand Economic: Growth, New York: 19e4,

A comparative examination of the available rate of return studies now seems appropriate in orderto determine what broader generalizations, if any, can be drawn from theml, Part It describes thestudios which are available, their temporal and geographic coverage, statistical base and representa-tiveness, and then reviews some of the major methodological problems encountered in comparing thesestudies, Part III compares the empirical results, and Part IV indicates what conclusions can be reachedand what the priorities should be for future research on this topic,

1. No effort is made to examine "shadow rates of return" generated through linear programmir, models, sees Psacharopoulos,G "Estimating Shadow Rates of Return to Investment in Education", land of Human Resources, Winta 1970, pp. 3440,

169

/20 t,

II

SAMPLE OF STUDIES

During the past few years I have accumulated approximately twenty rate of return studies, Whilenot systematic, the effort to colhot these studies has been at least partly deliberate, with an eye topreparing a paper of this sort; undoubtedly, there are other studies which have not come to my attention.While a few of these studies are for the United States and for other developed countries, the bulk of thornare for less-developed countries actively seeking to speed their rate of economic growth. Included arethe following countries: Kenya, Northern Rhodesia, Uganda, India (several studies), Philippines, Israel,Great Britain, Greece, Chile (several studies), Columbia (several studies), Mexico (several studies),United States (several studies), and Canada. Appendix Table A presents a full listing of these studies,indicating author, country, year and scope of the study, as well as the data base. Most of the studiesare for the late 1950's and early 1960's, although at least one extends back to the 1940's.

The extent to which these studies are comparable is not fully clear, For one thing, the coverage ofpolitical units varies considerably; though the analyses often are made at the national level, they areconfined in some cases to particular geographic areas within a country. Moreover, they frequently applyto specific sectors of the economy rather than the economy as a whole, whatever the geographical cov-erage. The reported levels of schooling usually differ somewhat because the structure of each country'sed,Acational system NrELL'ies. In addition, rates of return are not always available for certain levels ofeducation, in particular, for literacy versus non-literacy among the non-formally educated, and for dif-ferent types and amounts of post-secondary education. To further complicate matters the database for thestudies is rarely the same: some rely upon census-type data while others employ special survey datawhose quality no dote varies; some studies are based upon income and others upon earnings. Finally,the methodology for deriving the costs and return streams differs in detail even though the same generalapproach is usually followed.

Assessing the effects of these many differences on the comparability of the rates of return is amajor task, requiring a careful evaluation of eaoh study and ultimately a recasting of them on a com-parable basis. Since such an effort would, even if undertaken, still leave a good deal of uncertainty,we shall for the purposes of this paper assume that approximate comparability exists.

COMPARAI3ILITY

A number of more substantivk problems, aside from those just mentioned, arise in comparing theresults of the various studies. These problems can be grouped into four major categories: 1) use ofpresent value versus rate ot 4:um approach; 2) use of shortcut methods to estimate benefit streams;3) use of unadjusted data versus data adjusted for other non-school-related characteristics associatedwith earnings differences; 4) use of an economic growth factor in adjusting the cross-section age-earnings profiles. Each of these problems will be considered briefly. The three right-hand columns inAppendix Table B attempt to summarize for each study how these problems were handled.

1) Preserst Value versus Rate of Return

We shall use the rate of return criterion because most studies employ this rather than the presentvalue net ef cost. Moreover, the results arc rarely reported in enough detail to permit the calculationof present figures. It is often possible, however, to infer the general magnitudes of the rates of returnfrom present value figures, especially when the results are presented using several different discountrates.

A larger issue only touched upon here involves the underlying theoretical and empirical merits ofthe internal rate of return as compared to the present value. Alehianh, Hirsch1e1fer'1, and 13ailey1among others, have argued for the superiority of present value over rate of return, so as to avoidmultiple rates of return caused by the sometimes irregular behaviour of the age-education-earningsprofiles. But in a recent note, Jean4 demonstrates that some of the examples typically used to cast.doubt upon the rate of return approach represent rather special cases; he also shows which types ofage-cost-return streams yield indeterminate solutions. In most rate of return studies, the age-cost-return streams are not of the type that produce multiple solutions. In any case, however, the availabledata force us to concentrate on the rate of return.

2) Use of Shortcut Methods

An early problem in calculating rates of return arose because of the absence of age-earnings5 pro-files by levels of schooling. Although this problem diminished as more data became available, some ofthe early studies are flawed because the shortcut methods of constructing age-earnings profiles led toover or understatements of the rates of return.

One shortcut method assumes that average differenoes in earnings by level of schooling adequatelyreflect the actual pattern of difforenoes by age level. By ignoring the fact that earnings differences tendto grow with age - after the investment period these differences becomes increasingly large with age -the effeot is to increase the weight of benefits relative to costs and thereby to inflate the rate of return.The resulting overstatement of the rate of return will vary depending upon the extent to which earningsdifferences do increase with age. For example, Baldwin's° study of Northern Rhodesia uses this short-cut approach, although he builds in an offset to the overstatement that would otherwise occur. A some-what similar approach is followed by Shoup"' for Venezuela where he assumes constant differentials or,in some cases, builds in rather arbitrary increases in earnings with age.

The other method involves constructing synthetic age-earnings profiles, based on a variety of as-sumptions but relying heavily upon some observed age-earnings patterns for another region or country.Although this method could produce an over or understatement in the rates of return, the one casewhich has been examined - Harberger's° study for India - produced an understatement (Hansen9). Usinghis same assumptions on United States data for.1949, I found that, for four years of college, the syn-thetic data produced rates of return that ranged from one to almost two percentage points below

1. Alchian, A.A., "The Rate of Interest, Fisher's Rate of Return Over Cost, and Keynes Internal Rate of Return", AmericanEconomic Review, December 1955, pp. 938-943.

2. Hirschleifer, LA., "On the Theory of Optimal Investment Decision", journal of Political Economy, August 1958, pp. 329-352.

3. Bailey, M.J. , "Formal Criteria for Investment Decisions", Journal of Political Economy, October 1959, pp. 416-483.

4. Jean, W. H. , "Reply", Journal of Business, March 1069, pp. 99-100.5, We shall use the term "age-earnings" even though some of the aata are for "age-Income" profiles.

6, Baldwin, R. E., kgnon_210 p_t_rtand E o t Berkeley: University of California Press, 1968.

7. Shoup, C. S. , The Fiscal System aLyel_ig_t_ _Lie a Baltimore: Johns Hopkins Ness, 1969,

8, Hatherget, A.C, , "Investment in Man Versus Investment in Machine", In C.A. Anderson and M.J. Bowman, Eds., Ldg-

cationmid Economic Developmenb Chicago: Aldine, 1068, pp. 11-60.9. Hansen, W.!" , "Total and Private Rates of Return to Investment in Schooling", Journal of Political Economy, April 19631

pp. 128-141.

ve 0110d..)172 3, A

the actual rates of return, and, for four years of high school, the synthetic data prochwed rates of returnbetween three and one-half and four and one-half pereentage points below the actual rate of return. Thus,Harberger's rates of return could be understated by 8-17% for college and by 30-40% for high school,Offsetting this to some degree are the mortality effects which Harberger ignored but whose effects areless substantial, Kotharl's1 study which follows Harbergor's methodology undoubtedly contains similarbiases.

While the magnitude of error is likely to be smaller using synthetic profiles rather than flat profiles,1. e. those based on average differences in earnings of people with different educational attainments,we are in the somewhat more difficult position of not being certain whether the resulting rates of returnare too high or too low. In any case, however, the greater plentituclo of data has steadily reduced theneed for constructing synthetic ago-earnings profiles by level of schooling,

3) Other Adjustments

Initially, investigators had to work with whatever data were available, In the case of national orregional data, other important factors which might affect earnings differently by level of schooling couldnot be statistically controlled, such as family baokground, place of residence, etc). One way of obtainingwhat might be called "cleaner" estimates of the impact of echooling is to limit the sample to relativelyhomogeneous groups, though the cost is usually a great amount of information loss, The alternative isto use regression analysis to derive age-education earnings profiles which "hold constant" the effects ofother often important independent variables, Carnoy3,3 experimented with several different sets ofdata; one was unadjusted, another was adjusted for father's occupation, industry, city of occupation,and attendance, The latter reduced the differentials in earnings attributable to schooling, since someof these other variableb were correlated with schooling. Hanoch4,5 who carried out an even more elab-orate adjustment using the abundant data from the 1960 U. S, Census 1/1,000 sample, found a similarreduction in the earnings differential attributable to schooling, Data limitations ordinarily prevent ad-justments such as these, not to mention other desirable adjustments for differential ability and numerousother variables affecting incomes. Indeed, the adjustments for ability have usually been quite arbitrary,assuming that anywhere from zero to half of the observed earnings differences are due to ability andschool-related factors rather than to schooling as such (Denison" , Gounden7,5). Finally, and surpris-ingly, many investigators have made no allowance for expected mortality, differential unemploymentrates, or labour force participation patterns among groups with different amounts of schooling.

4) Economic Growth

While it is generally recognized that expected earnings will, because of economio growth, be greaterthan those indicated by cross-section age-earnings profiles, relatively few studies have made such ad-justments. It is cliffthult to know what the reason is, except that of convenience; however, Hollister3recently suggested that cyolioal fluctuations in economic activity aiCer age-earnings profiles differentlyfor people with different levels of school attainment. A simple "rule-of-thumb" correction calls foradding the assumed rate of per-worker economic growth to the rate of return calculated from cross-section data. We shall have to be content with such crude corrections until the needed longitudinal dataon education-age-earnings profiles become available.

1, Kothari, V.N.1 "Raurns to Education in India", mimeographed, University of Baroda, 1966.2, Carnoy, M,, "The Cost and Return eo Schooling in Mexico: A Case Study", unpublished Ph, D. dissertation, University of

Chicago, 1964,3, Carnoy, M., "Rates of Return to Schooling in Latin America",4, Hanoch, G., "Personal Earnings and Investment in Schooling", unpublished Ph. D. dissertation, University of Chicago, 1968,5, Hanoch, G., "An Economic Analysis of Earnings and Schooling", journal of_Human Resources, Summer 1967, pp, 310-329,6, Denison, E.E. The Sources of Growth in the U. S, and the Alternatives Before LI, , °pick,7, Gounden, A, M,11, "Education and Economic Development", Qpj8, Gounden, A. MN, . jweftrnent in akatio Juno opj_sit,9, Hollister, 11, , "Education and Distribution of Incomes Some Exploratory Forays", mimeographed draft, 1970,

123

III

THE NATURE OF INTERNAL HATES OF RETURN

In attempting to squeeze some meaning out of internal rates of return, it is important to rememberthat they capture at a moment of time the outcome of a whole series of past events and also reflect inpart future events. We can think of these rates as reflecting the interaction between the supplies of anddemands for different types of echtoated labour. The potential supply of labour was produced - and someis currently being produced - over several previous decades, The amounts produced as well as the fa-cilities available to produce them reflect, in considerable part, the past "market" for educated man-power. Similarly, the configuration of potential demand for educated manpower has built into it pastdecisions about the educational intensity of production, reflecting the relative scarcity of available pro-ductive inputs, as well as those underlying factors that generate the final demand for output producedwith educated manpower,

The supply and demand conditions also indicate in part future expectations. Even if present demandand supply appear to be in "balance", the prospects of sharp increases in either supply or demand in thenear future are going to affect earnings levels and hence measured rates of return. Similarly, sharpexpected increases in supply or demand can have effects on the costs of education and, hence, affuct therates of return independently of what might happen to future earnings levels.

Complicating all this is the fact that governmental policies may affect both the returns and the costs,and these policies may shift over time so that the prospects of disentagling the play of market forcesfrom policy effects is difficult. In addition, other "imperfections" in the market will obviously have abearing on the determinants of the rate of return through their effect on supply and demand.

The bare outlining of the factors which are "important" is of little help in interpreting rates ofreturn. What it does suggest is the difficulty of the task. Until there is more research on the natureof the educational labour market, including its dynamics, we are not in a strong position to say muchabout the underlying determinants of internal rates of return or of changes in them.

USES OF INTERNAL RATES OF RETURN

Customarily, and notwithstanding our lack of knowledge, internal rates of return have been used toassess the payoff to educational investment - to the individual as well as to society - relative to the payoffyielded by other forms of investment. The objective has been to say whether added investment in edu-cation should or should not be made. Much less attention has been given to the fact that rates of returnusually differ by levels of schooling and that the patterns of the rates have a bearing on the answer toquestions regarding the profitability of schooling investments. Hence, the purpose here is to focus onthe patterns of the rates of return, while giving little if any explicit attention to relative profitability.

:t1,24175

PATTERNS OF RATES OF RETURN

That any systematic patterns ocour in the "incremental" rates of return across oountrios is not fullyobvious from an inspection of the results of various oountries; by "incremental" (sometimes referred toas "marginal") we refer to rates of return on oaoh successive inorement of schooling rather than on largeblocks of sohooling, o. g, from sohool entry through high sohool, It may be helpful, therefore, to setout several general types of patterns and then olassify oountries aooerding to the type they fit moat closely.Tho following five typos of patterns appear oapable of capturing most of the variations observed:

Type Charaoteristio Pattern by Level of Educational Attainment

Constant rates of return across all levels of eduoational attainment,II Declining rates of return as level of educational attainment increases.

Ill Rising rates of return as level of eduoational attainment increases.IV Declining and then rising rates of return.V Rising and then deolining rates of return,

These patterns are shown in Figure 1,

Figure 1

ILLUSTRATIVE PATTERNS OF RATES OF RETURN

TO EDUCATIONAL INVESTMENT

Internal rate of return

0 4 8 12 16 20

Years of schooling

While greatly oversimplified, these patterns are of interest for their policy implications. Of course,what one concludes about the rates will depend on whether they refer to private or social rates of return)°,Lot us for purposes of discussion focus on the social rates of return. The first pattern (1) suggests a pol-icy of indifference as to which level should be expanded or alternatively argues for an across-the-boardchange; the second (II) indicates need for a greater concentration at the early years of schooling; thethird (III) suggests a concentration at the later years; and the fourth (IV) a concentration at both theearly and later years; and the fifth (V) a concentration at the intermediate years. Actually, the policyimplications of patterns III, IV, and V are more satle than just indicated, Given that education is asequential process, requiring the completion of lower levela of schooling prior to the higher levels,maximization of the rate of return to educational investment must take account not only of the incre-mental rates of return but also the rates of return over larger increments of education. To achieve ahigh rate of return at "say" the completion of high school, a steady flow of students through the lower andintermediate grades is essential even though the rates of return at these levels may be much lower, Toooften, however, education is viewed as a series of discrete steps, without recognition that the higherlevel of attainment requires completion of a whole series of steps, This argues for a focus on both in-cremental and average rates of return.

Utilization of the typology set forth above produces the classification shown in Table 1, which is ab-stracted in turn from the results prcsented in Appendix Table B. This classification is based on "social"rates of return, i, e, on total resources invested; where social rates were not available it became nec-essary to use the private rates. The importance of the level of disaggregation on the classification schemeshould be noted, the finer the breakdown by level of schooling, the greater is the possibility of undulatingpatterns. In some cases the rates for related levels of schooling (e.g. the first two years and the secondtwo years of college) were averaged in determining the patterns. To assist in the classification, sub-types IVa and Va were established to take account of double reversals in the rate of return patterns.

It is striking to note that most of the results are of Type II and Type V, with their respective patternsof declining rates of return, and of rising and then declining rates of return. A smaller number of studiesfall into Type IV, with only one country represented by Types I or III, Given the narrow range of school-ing over which estimates are available for great Britain (II) (only the upper levels) and Greece (III)(only the lower levels), it is difficult to be certain about the appropriateness of the classifications ofthese countries. And the estimate for Venezuela (IV), one of the earliest, is probably subject to con-siderable error, given the assumptions made in calculating the rates of return, This leaves us withTypesll, IV, and V. It is interesting to note that the Indian, Chilean, and Columbian studies fall intoTypes II and V. In view of the assumptions utilized in Harberger's Hyderabad study (V), we might wantto attach somewhat less weight to it, It is more difficult, however, to explain away the dual classifica-tion of the Chilean and Columbian studies,

EXPLANATIONS OF RATES OF RETURN PATTERNS

The limited number of studies, their lack of comparability, and the approximate nature of the re-sults preclude a systematic effort to explain the variety of patterns found and the placement of any coun-try in a particular category. Nevertheless, we can offer some preliminary speculations. To help or-ganize these speculations, let us advance several reasons why we would generally expect the rate ofreturn patterns to be as they ar0,

1, Social rates of return are defined here as reflecting all monetary benefits and all costs - the direct and opportunity costs tostudents plus the othes costs of education pald for by society,

2, Another intriguing question arises which cannot be discussed here t is it possible that questions regarding patterns and levelsare intertwined, ide, the relative pattern of the rates of return is related to the level of the rates of return to schooling or to the levelof the rates offered by alternative investment opportunities

1,46

TYPE

Table 1, CLASSIFICATION OF STUDIES ON RATES OF RETURNTO EDUCATIONAL INVESTMENT

Constant rates of return

II psslippi

Kenya, 1966 (Rogers)Bombay, 1956-67 (Kothari)India, 1960-61 (Gounden)India, 1960 (Selowsky)India Cities, 1964 (Reynolds)Great Britain, 1964 (Blaug)Santiago, Chile, 1962 (Bruton)Bogota, Columbia, 1963-66 (Selowsky)United States, 1949 (Hansen)United States, 1959 (Hanoch)

DESIGNATION OF STUDY

III Rising rates of return

Greece, 1960 (Liebenstein, in Bowles)Greece, 1964 (Liebenstein, in Bowles)

IV Declining and then rising rates of return

N. Rhodesia, 1960 (Baldwin)Israel, 1957-58 (Klinov-Malul)Venezuela, 1957 (Shoup)Canada, 1961 (Podoluk)

IVa Declining, rising, and then declining rates of return

Uganda, 1965 (Smyth and Bennett)

Rising and then declining rates of return

Hyderabad, India, 1957 (Harberger)Imus, Cavite, Philippines, 1966 (Williamson and DeVoretz)Chile, i958-59 (Harberger and Selowsky)Chile, 1964 (Selowsky)Bogota, Columbia, 1965 (Schultz)Columbia, 1961 (Gamacho, in Carnoy)

Va Rising, declining and then rising rates.of ivturn

Mexico, 1963 (Carnoy)Mexico, 1964 (Selowsky)

1) Influence of Cost-Return Relationships

The general tapering off of returns at the higher levels of schooling and the usually higher rates ofreturn at the early levels of schooling suggest that literacy and all that goes with the completion of a fewyears of schooling pays off rather well, but that diminishing returns soon begin to set in. Why should

178

tV;(1:7

this bo the case ? One important consideration is the cost struoturo, The total costs of education - Interms of both income foregone and the direct costs of schooling - rise rather steadily from elementaryschool up through college, Thus, on the basis of the overly simplified assumption that the returns to edu-cation riso by equal absolute amaunts per year of schooling, whiie costs rise by equal percentageamounts, the rates of return will in general fall with more schooling, Of course, these underlying costdifferences cannot provide a full explanation, since there is considerable variability in both the costand retura patterns.

2) InflujinotAlalmjattiLli_iMeehanisms

The fact that rates of return do'not always taper off more than they do may lie on the return side,particularly in developing countries. Because many highly educated people are. In the employ of.govern-Mente which ordinarilY have.rathel. rigidly prescribed salary schedules - schedules which are set by theeducated portion of the population -thebenefit stream may be abnormally high, Hence, this would hidethe full extent of any decline, Offsetting this no doubt is the fact that government employment ordinarilybrings with it a sizeable array of fringe benefits, most of which are nut captured in money wage data,Moreover, the prestige that goes along with government employment may add furthrif to any under-statement of the "true" rate of return for the better-educated, Which of these forees is strongest, wesimply do not know,

3) Supply and Demand Forces

The comments made thus far suggest that some constant, underlying forces are at work, and thatthese out rather uniformly across countries and time, An alternative view is that the rate of retvrnpatterns reflect in part at least the impact of unique supply and demand forces, so that, if we had sev-eral sets of comparably calculated rates of return for different years, we would expect to find changingpatterns. Put another way, the cross-section results may reflect disequilibrium conditions and so canbe explained by reference to other events affecting supply, demand, or both, Per example, changes inthe rate of a country's growth may give rise to differential increases in the need for people by skill andamount of schooling, If growth accelerates, then the stock of highly eduoated workers, for example,may be insufficient, with the result that wage levels will be bid up. This will trigger a response, oftena belated one, as additional people seek to obtain the types of education most needed; the result is toeventually push earnings and the rate of return back down again. Or, to take the opposite case, once aschool system is geared up to a larger production level, and given inadequate information on the relativesupply-demand situation, a larger number of people may enrol and eventually graduate than can be hiredat prevailing salaries; the result will be either declining relative salaries, unemployment, or possiblyboth. In general, then, an increased demand for better-educated workers would tend to raise rates ofreturn at the upper levels, and vice versa. This assumes that growth produces a rather education-specific pattern of demand for labonr; such an assumption about the pattern of demand seems quite ex-plicit in much of the work on educational planning iii developing countries. Presumably, the validity ofthis assumption could be examined with the help of education-occupation and/or education-industry ma-trixes. An increased supply of educated people will, on the other hand, depress rates of return. Whatall this adds up to is the conclusion that rate of return patterns, given the way rates are usually calcu-lated, are not unambiguous in the kind of information they provide,

179 .128

IV

ASSOCIATION WITH EDUCATIONAL DISTRIBUTION DATA

Given the emnhasis on educational distributions, it is appropriate to take the limited results wehave and see how they "fit" with the distribution data. The data on educational distributions are of twotypes, One type represents "stocks" and the other "flows". Distributions of educational attainment ofthe population or work force fall into the stock category, whereas distributions of school enrolments andenrolment rates more closely represent "flows", We shall examine both of these types of data.

Any effort to relate educational distribution data to rate of return patterns is complicated by whatwe think rate of return patterns reflect, One view is that rate of return patterns.reflect the outcomeof past decisions, whereas another is that they provide a signal of what is likely to happen, Hence, wemust quite carefully specify any expected relationships. If we adopt the former view, that the distribu-tions strongly affect rate of return patterns, we would expect to find an inverse relationship betweenrelative quantities (of educated people, students, etc. ) and relative rates of return. On the other hand,the notion that the distributions reflect a response to current and expected conditions, signalled by rateof return patterns, would lead us to anticipate a positive association between relative quantities and rel-ative rates of returns. We may find, therefore, that the rate of return patterns are consistent with oneor the other of these two views of the role of rates of return.

Let us begin by looking at the distribution of educational attainment. We shall initially assume thatrates of return reflect events of the recent past.. This suggests that on average we can expect to findrelative quantities and relative rates of return inversely related, More specifically, we would expectto finth I) heavier concentrations of people with post-secondary educational attainment in countries ofTypes II and V, 2) heavier concentrations of people with elementary attainment in countries of TypesHi and V, and 3) heavier concentrations of people with secondary attainment in Type IV countries. Thedata in Table 2 are not consistent with I) but they are generally consistent with 2) and 3). Thus, thedistribution and rate of return data Lit least partially support the notion that rates of return reflect re-cent investment outcomes, as reflected by the distribution of relative quantities of educated manpower.

It should Ix. clear that stock variables, such as data on the distribution of the educational attainmentof the population or work force, are probably not entirely appropriate. Recent flows may at the marginhave had a significant effect on earnings patterns and thus have altered rate of return patterns, Hence,flow variables are likely to be especially useful in casting light on rate of return patterns. If we takethe distribution of students in school to represent the flow variable, and if we think of these flows ashaving a dominant effect on rate of return patterns, then we would expect to observe the same patterns1), 2), and 3 discussed above. But Table 3 reveals clearly that the evidence does not support our ex-pectations, Indeed, secondary edueation is most heavily concentrated in Type II countries, and elemen-tary schooling shows a slightly heavier concentration in Type IV countries, On the other hand, there isno evidence of patterns the reverse of 1), 2), and 3) which would indicate people, through their enrolmentpatterns, are responding to rate of return patterns. We must therefore conclude that the flow data donot perform as we might have expected. Part of tho diffieuity may arise because the distribution ofschool enrolments is an imperfect measure of the flow of students out of the school system and into the labour

18

29

Table 2. PERCENTAGE DISTRIBUTION OF EMPLOYMENTBY LEVEL OF EDUCATIONAL ATTAINMENT

PRIMARY SECONDARY POST-SECONDARY

L

II. Kenya - -.:.

India 97 2 1

Groat Britain 52 40 7

Cohunbia - - -United States 53 27 19

III. Greece 89 8 3

IV. N. Rhodesia - - -Israel 55 32 13

Venezuela -Canada 35 56 9

IVa. Uganda 92 7 1

V. India 97 2 1

Philippines 80 14 6

Chile 93 4 2

Columbia - - -

Va. Mexico 93 5 2

SOURCE: Organisation for Economic Co-operation and Development, 1966.

Table 3, PERCENTAGE DISTRIBUTION OF SCHOOL ENROLMENT 73Y LEVEL OF SCHOOLING....--

PRIMARY SECONDARY POST-SECONDARY,

I.

II, Kenya 97 3 oIndia 62 36 2Great Britain 43 55 2Columbia 87 11 3

United States 69 23 8

III. Greece 77 21 2

IV. N. Rhodesia 99 1 0Israel 85 12 3

Venezuela 86 10 4Canada 77 20 3

IVa. Uganda 78 21 1

V. IndiaPhilippines 78 13 8

Chile 81 16 2

Columbia 87 11 3

Va, IVIekico , , , , ,,,,,,,,,,, 97 6

BOUM UNESCO Current School Enrolment Statistics,

,1,2

130

force. Nor do such data tell much about either the possible queueing of people who desire either to enterthe educational system or to proceed through ever-higher levels of the system. Nor do they tell aboutthe effect of unemployment in whetting or dampening the desire on the part of young people to securemore education,

A further possibility is to look at enrolment rates rather than the distribution of enrolments, so asto better reflect the size of the flow relative to the stook of educated workers. The enrolment data arepresented in Table 4. Our expectations would be identical with those earlier - high enrolment ratesand low rates of return - if we expect the flows to have affected the ourOnt pattern of rates of return.The evidence in support of expectation 1) is not apparent, nor is it apparent in support of expectations2) and 3).

Table 4. ENROLMENT RATES BY LEVEL OF SCHOOLING

PRIMARY SECONDARY POST-SECONDARY

I.

II. Kenya 53 4 0.0India 32 22 1.4Great Britain 61 105 4.9Columbia 46 17 1.8United States 81 80 33.9

III. Greece 62 44 3.5IV. N. Rhodesia - - -

Israel 78 49 10.2Venezuela .

71 30 5.1Canada 90 61 9.0IVa. Uganda 32 6 0.2

V. India 32 22 1.4Philippines 56 25 9,7Chile 69 35 1 3.5Columbia 46 17 1.8

Va. Mexico 57 11 3.1

SOURCES Columns 1-2, UNESCO, 1986, Table 4, and Column 3 based on data from UN, Demographic Yearboajg UNESCO, 1'..66

183 131

CONCLUSION

This analysis has brought out the fact that the patterns of rates of return to educational investmentfor the most part either fall with more schooling or first rise and then fall. But we have been able toshow at best a weak association between these patterns and the educational structure, either as reflectedin educational attainment data or in enrolment patterns. Several factors account for these rather disap-pointing findings. First, the models that we possess to explain the observed distributions of most vari-ables are extremely primitive; although we can fit functions of one kind or another to such distributions,we are unable to say much about the forces which generate them. Second, in the absence of any sub-stantial analytical scheme, one can only search for empirical regularities, as has been tried here.But because the sample of rate of return studies is still so small, this search has necessarily been acrude and exploratory one.

In future work on this topic, several steps must be taken. The first is to augment the supply ofrate of return studies, preferably by assembling additional studies which have already been completedbut are not included here. The second and more difficult is to produce more and better data on educa-tional distributions so as to fill the existing information gaps. We need additional data on both stocksand flows. In particular, we require data that reflect what is going on at the key junctures in the edu-cational system (continuation rates by level of schooling), and what is happening at the point where theeducational system and the labour market join together (unemployment rates by level of school attain-ment for new and recent entrants into the labour force). Finally, we need unemployment rates by levelof school attainment for those people already in the labour force. The third and still more difficult taskis to develop a comprehensive set of hypotheses that seek to explain differences in rate of return patternsso 'ilat these hypotheses can be subjected to empirical testing. This requires going beyond using onlyeducational distribution data. In addition, variables reflecting demand conditions must be introduced,so as to capture the critical supply and demand factors which are at work. As a result of such work itshould be possible for us to gain a better understanding of the determinants of rate of return patternsand their link to the underlying quantities of educated manpower. In the meantime, we am left with anintriguing set of observations that begs for an explanation.

185

132

Appendix Tables A and B

PATTERNS OF RATES OF RETURN TO INVESTMENT IN EDUCATION:SOME INTERNATIONAL COMPARISONS

W. Lee HansenUniversity of Wisconsin

March 1970

133

Table A. SUMMARY OF STUDIES ON RATES OF RETURN TO EDUCATIONAL INVESTMENT

AUTHOP, DATE,AND REVERENCE

YEAR OF STUDY,LOCATION;

AND TYPE OF WORKER

TYPE OF DATAMETHODS USED

IN CONSTRUCTIONOF BENEFIT STREAMS

CONTROLS AND

ADJUSTMENTS,

AND ADJUSTMENTSFOR ECONOMIC GROWTH

AFRICA

Baldwin, (3) 1960, NorthernRhodesia

Urban males Average wage levelswithout regard to age.

Rogers, 1968 (39) 1966, Kenya; civilservants and teachers,

Government pay scalesfor civil servants andteachers.

No information, Assumed a standardincome by educationallevel.

Smyth and Bennett,1966 (48)

.

1965, Uganda Public salary scalesgrossed upward to ac-count for higher salaryscales in private sec-tor.

Age-earning curvesare linear exponentialcurves derived by in-speetion from theGovernment scales.

Adjustment for alter-native entry to wage orfarm employment.

ASIA

Gounden, 1965 (16, 17) 1960-61, India, urbanmales and engineers,

NCAER survey of 5,000urban males, CSTRstudy of 4,000 engi-neers.

Age-income streamstaken directly fromaverage annual incometabulated by age andeducation level.

Arbitrary adjustmentof 50% to account fornon-educational deter-minants of income.

Harberger, 1963 (22) 1957, Hyderabad,India; male earners.

Sample of 5,885earners distributed byearnings and schooling,

Assumed age-earningprofiles with the fol-lowing form: 1) peakin earnings reached ata later age for succes-sive educational levels2) peak earnings werea higher fraction ofaverage earnings forsuccessive educationallevels.

Adjusted for labourforce participation.

Kothari, 1966 (31) 1956-57, Bombay City,India.

3% random survey oftenements in GreaterBombay, earnings byeducation level.(not by age),

Estimated an age-earning profile withsimilar assumptionsas Harberger plus as-sumption that earningsdecreased after age 35.

Correction for survivalrates of cohorts by edu-cational level would re-duce rate of returnby about 2%.

Reynold9, 1968 (38) 1964, Bombay,Jamshedpur, Madras,and Rowkela; urbanmales.

Sample of 1,800 prod-uction workers in steeland metal-workingfirms.

Age-education-earnings data takendirectly from surveyresults,

Selowsky, 1967, (45) 1960-61, India; urbanmales and engineers.

Gounden's data.

---..--

Gounden's age-incomeprofiles (includingcosts),

Attributed 100% of thewage differential toeducation rather thanone half as did Gounden

Table A. (cont'd) SUMMARY OF STUDIES ON RATES OP RETURN TO EDUCATIONAL INVESTMENT

A DATEUTHOR, ,

AND REFERENCE.

YEAR OF STUDY,LOCATION;

AND TYPE OP WORKERTYPE OF DATA

METHODS USED

IN CONSTRUCTIONOF BENEFIT STREAMS

CONTROLS ANDADJUSTMENTS,

AND ADJUSTMENTSFOR ECONOMIC GROWTH

ASIA (cont'd)

Williamson and 1966, Imus, Cavite A Population Institute Y,egressions made of Attributed 50% ofDeVoretz, 1967, (M) (Philippines); male survey. The sample income on the age differential to ecluca-

heads of households, size was 1,003 andgives average annualincome by age andlevel of schooling,

variable for each edu-cation level to yield anage-earnings profile.

tion: Used mortality. adjustment,

EUROPE AND MIDDLE EAST

Blaug, 1967, (7,8) 1964 and 1967, 2 surveys: a) 1964, 1st survey; earning Assumed that 0.6 ofGreat Britain a) male random sample of differentials by pres- observed differentialworkers; b) profes- 6,500 male heads of ent age are calculated; associated with extrasional, managerial andskilled workers.

households; b) 1967,sample of 2,800

2nd survey: agef-earnings profiles are

education is due toeducation for lst sur-

workers in British obtained from the vey. No adjustmentauto industry and 4large electricalengineering firms.

data, for ability, socialclass, etc. used for2nd survey.

Klinov-Malul, 1966 1967-68, Israel, a) survey of 3,000 Calculation of the net Results standardized(30) a) Jewish urban families - wage and effect of education for for continent of origin

workers - heads of salary income by the population of each and length of residence.households education. continent-residence Alternate calculationsb) professionals b) sample survey of 4 combination; erime- of individual returns at

professionals (1,000). times utilizing stan-dardization and leastsquares methods. '

a 3% annual growth inGNP.

Leibenstein, 1967, 1960, 1964, Athens, Sample size of 2,700, Age-earnings profiles Assumes alternative(32) Greece; male workers

and female workers,plus salary informatioron public workers andprofessional organi-zations,

are constructed,Taken directly fromdata.

annual growth ratesof 0, 4, and 5%,

LATIN A MERICA

Bruton, 1967, (9) 1962, Greater Santiago,Chile; male membersof labour foree,

Data on education, age,and wage income (2, 60fobservations - a num-ber of which wereexcluded).

Earnings are re-grossed on educationto yield a wage-educa-tion relationship,Age-earnings profilesare developed.

Camacho, 1964, (11) 1961, Columbia urban,males.

No information. No information,

Harberger andSelowsky, 1966 (23)

1958-59, Chile, maleand female,

Sample size is notspecified.

Age-earnings profilesare not constructed,rather they asstunethat the differentialbetween the earningsof the educationgroups is relativelyconstant as a functionof ago.

189

41[35

Table A, (cont'd) SUMMARY OF STUDIES ON RATES OF RETURN TO EDUCATIONAL INVESTMENT

AUTHOR, DATE.AND RFPERENCE

YEAR OF STUDY,0RUC1,CATIONAND TYPE OF WORKER

TYPE OF DATAMETHODS USED

IN CONSTTIONOF BENWIT STREAMS

CONTROLS AND

ADJUSTMENTS,AND ADJUSTMENTS

FOR ECONOMIC GROWTH

LATIN AMERICA (cont'd)

Schultz, 1968, (41). .

1965, Bogota,Columbia

Sample Size: 684 men,314 women, Bothhourly and weeklyearnings by age andeducation.

Regression estimates-of age-log earningsprofiles by level,

Adjustment for rnigra-tion to Bogota:

Shoup, 1950, (4'7) 1950's, Venezuela Sample data Based on assumedshapes of age-earningsprofiles,

Selowsky, 1967, (45) 1964, Chile; urbanmales.

No information. Age-earning profile in"Encuesta Nivel diVida" centro de Plant-ficacio'n Economica,Universidad di Chile,1964.

Selowsky, 1968, (46)

1

1963-66, Bogota,Columbia; urban malesand females.

Hourly wage data byschooling and age takenfrom unemploymentsamples. 10, 715observations.

Age-earnings profilesfrom data.

,

Five versions calcu-lated with adjustmentsfor L. F. participationrates, unemployment,changes over time.Version 5 - adjustmentfor growth in L. F.and gross domesticproduct.

NORTH AMERICA

Carnoy, 1964, (12, 13) 1963, Mexico City,Puebla, and Monterey,Mexico; male wageearners in 8 occupa-

3,901 observations,data on wage andsalary, schooling inyears, age, father's

Earnings are regressedon schooling, age, oc-cupations,father's oc-cupation, etc. ; sample

Controlled for father'soccupation plus othervariables (indubay,city).

tional classes, occupation, disciplineof study, and industry.

then divided into school-ing levels which per-mitted analysis withineach category. Promthese results lifetimeearnings streams areconstructed.

Rano* 1967, (21) 1959, United States,males, white and non-white for North andSouth.

1960, Census data. Used mean age-education-income data,adjusted for variablescorrelated with age.

Hansen, 1963, (18) 1949, United States,males,

1950, Census data. Used mean age-education-incomefigures,

Adjusted for mortality.

190

Table A. (cont'cl) SUMMARY OF STUDIES ON RATES OF RETURN TO EDUCATIONAL INVESTMENT

AUTHOR, DATE,AND REFERENCE

YEAR OF STUDY,LOCATION;

AND TYPE OF WORKER

TYPE OF DATAMV,TIIODS USED

IN CONSTRUCTIONOF BENEFIT STREAMS

CONT,NOLS AND

ADJUSTMENTSI AND ADJUSTMENTS

FOR ECONOMIC GROWTH

NORTH AMERICA

Podoluk, 1965, (36) 1961, Canadian males. 1961, Census data. Used average age-education-earningsdata.

.

Selowsky, 1967, (45) 1963-64, Mexico. Used Carnoy's sample Adjustment for ex- Adjusted for expectedand a sample from pectedlabourforcepar- annual growth rate ofthe "Direccion de ticipation, unemploy- wages of level ofMuestro". ment, and survival

rate.schooling.

191 11.37

Table 13, SUMMARY OP RATE OP RETURN ESTIMATES

CIT Y, COUNT'n , AND YEAR LEVEL OP SCHOOLING

RATE OF RETURN

SPECIA L NOTESPRIVATE SOCIAL

API ICA

Kenya, 1966 (30) 4th form plus 38

(Roge rs) 9 months governmentaltraining/4th form6th form/4th form negative4th form plus 2 yearsprimary teacher training/4th form 10. 64th form plus 3 yearssecondary teacher training/4th form plus primaryteacher training 30, 04th krm plus secondaryteacher training/6th formun1versity/4th form plus

42, 0

secondary teher training 19. 0university/Oth formunivers4ty/4th form plus

26. 0

primary teacher training 24. 5

Northern Rhodesia, 1060, (3) Standard I/0 13

(Baldwin) Standard II/I 11

Standard III/11 4

Standard IV/111 15

Standard V/1V 16

Standard VI/V 22

Estimates from gresent value results

Uganda, 1965 (48) primary (7)/0) 66

(Smyth and Bennett) CSC(11)/P(7) 22

HSC(13)/CSC(11) 78

university(16)/HSC(13; 12

ASIA

Assumption of no Inemploy-ment; earnings includehousing subsidy; personsbegin entering the work forceat age 18 and retire at age 55;private direot costs for higherlevels in Kenya is zero; costsinclude foregone earnings andthe individual and the statedirect costs.

Assumes constant earningsdifferenees; costs includeforegone income and schoolcosts; disoounts over 45years, in recognition of up-ward bias imported by as-sumption of constant earningsdiffe misses.

Earning flows for primaryeducated manpower are onlyestimates; cost data includeforegone earnings, capitalrepayment on eduoation plant,reourring operating costs,interest foregone (and the costof educating those who do notas aminatioris

Imus, Cavite; elementary(7)/illiterates 9 8 Cost data is from 1965 ex-Philippines, 1966 (54) high school/elementary 29 21 trapoled to 1966; it includes(Williamson and DeVoreta) college/high school 12 11 direct expenditures and earn-

ings foregone for the privateestimates plus governmente enditures for social costs.

Bombay City-, India, high school (12)/middle (8) - 20 It was necessary to estimate1956-57, (31) college (17)/(12) 14 13 the age structure of the(Kothari) engineering (17)1(12) 25 22 earners and to isolate the

arts and !V ienoets (17)/(12) 10 influence of business andcommercial owners underthe assumption that educa-tion only marginally influ-enced their earnings.

vilimmilM.Elililifiliialil

Table 13, (coed) SUMMARY OP RATE OF RETURN ESTIMATES

cry, COUNTRY, ANI) YEAR LEVEL OP SCII0OhING

RATE OF RETURN

PRIVATE SOCIALSPECIAL NOTES

ARIA (coned)

Hyderabad, India, 1957 secondary (12)/primary (8) 11. 9 Sample was heavily weighted(22) college and university (18)/S 16. 9 with younger people so sample(Harberger) (12) was roweightoci: data referred

secondary plus oollege/P (8) 15. 0 to people with some primary,etc. so it was necessary to esti-mated average income of co m-pleters; assumptions madewere likely to produce over-estimates for rates of return;cost data; earnings foregoneand assumed direct costs(conservative).

India, 1060 (5)/(2) 23. 5 2l. 2(45) (8)1(5) 17. 7 19. 9(Se lowsky) (11)/(8) 16. 4 18. 9

(15)1(11) 11. 0 16. 2(17)/(15) 14. 7 16. 0

India, 1060-61 literates/ illiterates 30 15. 9 It was not always possible to(16,17) primary (5)/literate 23. 0 17. 0 isolate earnings figures from(Counclen) middle (8)/P (5) 13. 0 11. 8 income figures; those with

matriculates (12)/M (8) 10. 0 10, 3 primary education and belowbatch, degree (15)/M (12) 8. 1 7. n enter the labour force at ageengineering (17)/M (12) 13. 5 9. 8 12 and retire at ago il0; as-engin, (17)/bach. (15)

.

20. 5 9. 7 sumes full employment; costdata include direct expendi-tures, depreciation of physicalassets, imputed value of inter-este, and foregone earnings;gross investment in educationforms 8. 6% of adjusted NYand 44, 1% of gross physicalcapita: formation,

India Cities, 1964 primary (5)/literate 21, 0 14, 5 Cost data based on updating(38) middle (8)/primary (5) 12, 0 9. 1 of Gounden data from 1961;(Reynolds) matriculate (12)/middle (8)

two years college (24)/11. 4 7, 0 based on earnings data to

age 60.matriculate (12) 4. 4 1, 8

EUROPE

Ornat Britain, (6,8) terminal education age 13 12. 5 1st survey; no distinction bet1964 (10-18) 14 8 wean. types of schooling or(13laug; (15-21) between full- and part-time

schooling; breakdown by ageis too largo to allow stanodarclization,_,..

103

; 139

Table 13. (oont'd) SUMMARY OF RATE OF RETURN ESTIMATES

CITY, COUNTRY, AND YEAR LEVEL OP SCHOOLING

RATE OF RETURN

Great 4ritain, (oont'd)1007

Level of QualificationRoyal Society of Arts, andCity and Guild Institute ofLondonpreliminary certificates

General Certificate- ordinary level, RSAadvanoed and COL inter-mediate certifieate

General Certificate- advanced 1eel, ordinarynational certificate andordinary national diploma

Higher National Certificate,COL full technical certificate,

university degree, highernational diploma

university degree (honours),diploma in technology

Greece (32)1960

1964(Liebenstein)

12/6 (male)15/615/12 "15/6 (female)

12/6 (male)15/8 "

15/1212/6 (female)

PRIVATE SOCIAL

5

8

(6)

( /8)

5.(5.

8.(15)

5

5)

5

8 (1. 5) 7 (0)

9. 5 (15) 7. 5 (12)

8. 5 (7) 8 (5)

9. 5 (10) 8 (8)

4. 5 (9)8 (10)

8 (12. 5)3 (7)

3 (7)

5 (9. 5)8 (12. 5)5 (9. 5)

SPECIAL NOTES

2nd survey; more detailed in-formation on type and levelof education; social rates ofreturn are calculated frombefore-tax earnings with costdata as the total resouroeoasts including Income fore-gone; the private rates ofreturn are calculated fromafter the earnings and reflectonly private coats.

Figures not in parenthesesrefer to comparison withschool-leaving age. Figuresin parentheses refer to com-parison with previous level.

The survey collected data oneach worker's age, years ofeducation (both technical andgeneral), monthly earnings,and occupation.

Figures in parentheses as-sume a 4% rate of economicgrowth.

Israel, 1957-58(30)(Klinov-Malul)

(Present Values, IL thousands; 8% discount rate)

PRIVATE

Primary 11. 3Secondary(discount rate 10%) (-4. 0)Higher EducationEngineers 1, 3

Lawyers -1. 0CPA's 42. 9Physicians -24. 9

1464

SOCIAL

SOCIALADJUSTED

FOR 3,4 GNP

9. 4-O. 8 +5.

(-4. 0)

6, 1 2. 7

5. 3 16. 4-0. 2 3. 1

25. 9 82, 7

. 6 -13.

Income tax is used as apartial measure of returnsto society; the income ofyounger professional workersis rising relative to olderworkers. This change inthe structure of income byage is somewhat peculiarto Israel (due to immigration)and is refleuted even morestrongly in the present valueof incomes; cost data in-elude expenditures by society(salaries and wages, books

Table B. (cont'd) SUMMARY OF RATE OF RETURN ESTIMATES

CITY, COUNTRY, AND YEAR LEVEL OF SCHOOLING

RATE OF RETURN

SPECIAL NOTES

PRIVATE SOCIA L-Israel, 1957-58 (oont'd)

-and materials, depreoiationin buildings) and the pOvateexpenditures of indivkluals(income foregone, tuition andfees, and books and materials).

LATIN AMERICA

Chile, 1958-59(23)(Harbergor and Solowsky)

primary (average 5. 5 yeard)/none "special" secondary(average 8. 5 years)secondary (average 11. 5years)university

24, 0

29. 0

16, 912. 2

Cost data is from $ and #?vet', "The Cost of Educationin Chile", (Universklad Cato-Heft de Chile, 1950),(mimeographed).

Chile, 1964 2/0 7, 7 7. 7 Used cost data of Yver.(46) 4/2 19. 1 13. 4(Selowsky) 6/4 24. 8 17, 2

8/6 12. 4 16, 012/10 22, 9 15. 3

Santiago, Chile, 1962 primary (6)/none 18 (16, 5) Income data is a byproduct(9) secondary (12)/primary 18 (18) of a survey on unemployment(Bruton) university (17)/secondary 14 (14) conducted by the Institute de

(figures in parentheses include the costs of educating all Eeonomia, Universidad depersons attending school whether they finish or not) Chile; cost data is from Raul

E. Yverts study and includedirect current outlays inteacher salaries, books andsupplies plus rental value ofsehool building, grounds andequipment plus foregone earn-ings,

Bogota, Columbia (all RofR are social) A 1 A Costs Include earnings fore-(46) 1063-66, primary (3)/illiterates 32 28 28 gone, payments to teachers(Selowsky) primary (6)/Illiterates 33 28 30 and depreciation and interest

bachillerato (11)/B (8) 23 24 25 of educational equipment.B (11)/B (10) 21 21 23 Version:university (16)/B (11) 6 6 7 2) adjusted for L. F. partiel-university (14)/B (11) neg. neg. neg. pation rates; assume full

employment3) adjusted for unemploymentwhich is substantial in lowwage groups5) assumption of growth overtime in labour force and GDP...

Bogota, Columbia, 1065 Primary (3)/tione 18. 2 15, 3(41) secondary (11)/P (5) 34, 4 26. 5(Schultz) vocational (8)/P (5) 51. 6 35, 4

university (10)/S (11) 4, 5 2, 0

Table 13, (ooni'd) SUMMARY OF RATE OF RETURN ESTIMATES

CCY, COUNTRY, AND YEAR LEVEL OF SCHOOLING

RATE OF RETURNSPECIAL NOTES

PRIVATE SOCIA L

Columbia, 1961(11)(Camaoho)

primary (5)teohnioal secondary (11)general secondary (11)university

20193010

Venezuela, 19s7(47)(Shoup)

primary (0)/illiterates7-1112-10

8217

23

Earnings foregone are notincluded in cost estimates ofthe primary rate whioh woulcilower the rate to approx. 30%.

NORTH AMERICA

Canada, 1961(36)(Podoluk)

elementarysecondaryuniversity

16. 316. 319. 7

Assumes no unemployment,

Mexico, 1963(12, 13)(Carney)

2-45-67-8

21. 148, 636, 5

17. 337. 523. 4

Private costs include directexpenditures on tuition, books,transportation, Impplies, etc.

unadjusted 9-11 17, 4 14, 2 plus earnings foregone; social

12-13 15. 8 12. 4 costs originate in a study of

14-16 36, 7 29. 5 public expenditure on formalsohooling in Mexico - 1940-1962; it includes implied rentand depreciation changes forbuildings.

2-4 15, 2 12. 8

father'sincome

5-67-89-11

44. 931, 0

34, 520. 6

constant 12-13 14, 6 11. 4

14-16 39. 6 31, 5

Mexico, 1964 4/0 (marginal) 17. 8 17. 3 Adapted from Carney's

(45) 6/5 37, 3 24. 3 results,

(Selowsky) 7-8/6 24. 0 (total -9-11/7-8 15, 1 22. 5 Carnoy's12-13/9-11 14, 4 data)

14-16/12-13 29. 9 21. 4

United States, 1949 2/0 89 Assumes no unemployment.

(18) 6/2 14, 6 Costs include all of usual

(Hansen) 8/6 29. 2 components,

10/812/10

12, 718, 6

9. 613, 7

11. 4

14/ 1216/14

6, 218. 7

5. 415. 6

10, 2

United States, 1959 4/0 (white North) 100. 0 89. 0 Assumes no unemployment;

(20,21) 6/4 21. 8 6, 0 no adjustment for mortality.

(Hanooh) 8/6 16, 3 10, 0

10/8 16. 0 12. 0 (n n-white12/10 7. 1 7, 0 South)

14/ 12 12, 2 7. 0

16/14 7, 0 5. 0

REFERENCES

1, Alohian, A. A, , "The Rate of Interest, Fisher's Rate of Return Over Cost, And Keynes LiternalRate of Return", American Economic Review, December 1955, pp. 938-943.

2. Bailey, M. J. , "Formal Criteria for Investment Decisions", Journal of Political Economy,October 1959, pp. 476-483.

3. Baldwin, R. E. , Economic Development and Export Growth Berkeley: University of CaliforniaPress, 1966.

4. Becker, G. S. , "Underinvestment in College Education", American Economic Review, May 1960,pp. 346-354.

5, Becker, G. S. , Human Caeital, Princeton: Princeton University Press, 1964.

6. Blaug, M. , "The Rate of Return on Investment in Education in Great Britain", Manchester School,September 1965, pp. 205-262.

7. Blaug, M. , "Approaches to Educational Planning", Economic Journal, June 1967, pp. 262-288.

8. Blaug, M. , "The Private and the Social Returns on Investment in Education: Some P.esults forGreat Britain", The Journal of Human Resources, Summer 1967, pp. 330-346.

9, Bruton, H. J. , "The Productivity of Education in Chile", Center for Development of Economics,Williams College, Research Memorandum No, 12, 1967.

10. Bowles, S. , Nanning EducationalSystems for Eonomic Growth, Harvard: Harvard UniversityPress, 1969.

11. Camacho, G. F. "Rendimento de la Inversion en Educaoion en Colombia", Bogota: CEDE,Universidad de los Andes, July 1964; Cited in Carnoy (1967) p. 363.

12, Carnoy, M. $ lbe Cost and Return to Schooling.hylexico: A Case Stud , unpublished Ph, D,dissertation, University of Chicago, 1964,

13, Camay, M. , "Rates of Return to Schooling in Latin America.' Journal of Hutnan Resources,Summer 1967, pp. 359-374.

14, Denison, E. E, naurauuszyttuLtea jaiLAujaLl.9 ttyfirfoie_U Washingtir,D, C, Committee for Economic Development, 1962.

15. Fabricant, 8 Basic Facts on Productivity Change, New York: National Bureau of EconomicResearch, 1959,

16. Gounden, A. M. N. , Education and Economic Development, unpublished Ph. D. dissertation,Karukshetra University, Indif., 1965,

17, Gounden, A. M. N. , "Investment in Education in India", Journal of Human Resources, Summer 1967,pp. 347-358.

18. Hansen, W. L. , "Total and Private Rates of Return to Investment in Schooling", Journal of Po litiehlEconomy., April 1963, pp. 128-41.

19. Hansen, W. L. , Comment oD.Harberger's Estimate of Rate of Return to Investment in Education inIndia, mimeographed, August 7, 1963.

20. Hanoch, G. , Personal Earnings and Investment in Schooling, unpublishcd Ph. D. dissertation,University of Chicago, 1965.

21. Hanoch, G. , "An Economic Analysis of Earnings and Schooling", Journal of Human Resources,Summer 1967, pp. 310-329.

22. Harberger, A. C. , "Investment in Man Versus Investment in Machine", in C. A. Anderson andM. J. Bowman, eds. , Education and Economic Development, Chicago: Aldine, 1965, pp. 11-50.

23. Harberger, A. C. , and Selowsky, M. , The Key Factors in the Economic Growth of Chile: AnAnalysis of the Sources of Past Growth and of Prospects for 1965-70, mimeographed, CornellUniversity, 1966. Also cited in Carnoy, 1967, p. 368.

24. Harbison, F. , and Myers, C. A. , Education Manpower, and Economic Growth, New York:McGraw-Hill, 1964.

25. Hirochleifer, J. A. , "On the Theory of Optimal Investment Decision", Journal of PoliticalEconomy, August 1958, pp. 329-352.

26. Hollister, R. , Education and Distribution of Income: Some Exploratory Forays , mimeographeddraft, 1970.

27. Jean, W. H. , "Reply", Journal of Business, March 1969, pp. 99-100.

28. Johnson, H. G. , "Observations" in Organisation for Economic Co-operation and Development,The Residual Factor in Economic Growth, Paris 1964, pp. 219-227.

29. Kendrick, J. W. , hioduotivitie U. s, , Princeton: Princeton University Press, 1961,

30. Klinov-Malul, R, , The Profitabilit of Investment in Education in Israel, Jerusalem: FalkFoundation, 1966.

31, Kothari, V. N. Returns to Education in India mimeographed, University of Baroda, 1966.

32, Leibenstein, N. $ "Rates of Return to Education in Greece", Development Advisory Service ,Harvard University, .Qm,19_p_iyglgpmak.p_oiNt o. 94, September 1967, p. 13. Also citedin Bowles, 1969, pp. 153-156.

33. Myrdal, G. $ Asian pliuna, New York, 1968, Vol. M.

198

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34, Organisation for Economic Co-operation and Development, Statistics of the_paclipatimiinsticlu-()atonal Structure of the Labour Force in 53 countries , Paris 1969,

35, Pandit, H. N. , Enductivity of Investment in Education; the Conceptual Framewor. Techniques,and Major Finding!, New Delhi; National Institute of Education, 1969.

36. Pociohlk, J. H. , Earnings and Education, Ottawa: Dominion Bureau of Statistics, 1964.

37, Psachitropoulos, G. , "Estimating Shadow Rates of Return to Investment in Education", Journalof Human Resources, Winter 1970, pp, 34-50.

38. Reynolds, M. , "Some Evidence on the Return to Schooling in Indian Industry", unpublishedmanuscript, October 1968.

39, Rogers, D. C. , The Returns to Investment in Higher Leyekof Educa0on in Kenya, Institute forDevelopment Studies, University College , Nairobi, 1968,

40. Rogers, D. C. , Private Rates of Return to Education in the United States: 4 Case Study,unpublished Ph. D. dissertation, Yale University, 1967,

41. Schultz, T. P., "Returns to Education in Bogota, Columbia", RAND Corporation, MemorandumRM-5645-RC/AID, September 1968.

42, Schultz, T, W. , "Investment in Man; An Economist's View", Social Science Review, June 1959,pp. 108-117.

43, Schultz, T. W. , "Education and Economic Growth", In N. B. Henry ed, , Social Forces InfluencingAmerican Education, Chicago: University of Chicago Press, 1961, Part II, pp. 46-88,

44. Schultz, T. W, , "The Rate of Return in Allocating Investment Resources to Education", Journalof Human Resources, Summer 1967, pp. 293-310.

46. Selowsky, M. "Education and Economic Growth; Some International Comparisons", Proiectior .1Quantitative Research in Economic Development, Harvard University, Economic DevelopmentReport No. 83, November 1967.

46. Selowsky, M. , "The Effect on Unemployment and Growth on the Rate of Return to Education;The Case of Columbia", Pro ect for Quantitative Research in Economic Develo ment HarvardUniversity, Economic Development Report No. 116, 1968.

47. Shoup, C. S. , The Fiscal System of Venezuela, Baltimore: Johns Hopkins Press, 1959.

48. Smyth, J. A. , aid Bennett, N. L. , "Rates of Return on Investment in Education: A Tool forShort-Term Educational Planning, Illustrated with Uganda Data", In G. Z. P. Bereday and J. A.Lauwerys, eds., 1_,M_World, Year &A on Educatim, "Education Planning", New York: Harcourt,Brace and World, 19671 pp. 299-822,

49. Solow, R. M Capital Theory and the ltate of Return, Amsterdam: Rand McNally, 1963.

60. UN, Demographic Yearbook, (various years),

U. UNESCO, World Surve of Education, Paris 1966, Vol. IV.

61 UNESCO, Currentnet tatisti s, (various years).

145199

53, Williamson, J. G. , "Economic Growth in the Philippines: 1947-1965: The Role of TraditionalInputs, Education, and Technical Change", Institute of Economia Development and Research,School of Economics, University of the Philippines, Discussion Paper No. 67-8, September 12,1967.

54, Williamson, J, G. , and DeVoretz, D. J "Education as an Asset in the Philippine Economy",In M. B. Conception, ed, , Phili ii_pp_.,1.ii3_1t..,_tlatislintheAtycantiejl, Manila: Community Publishers,Inc. , 1969, pp. 133-168.

Paper 5

THE SEARCH FOR EQUITY IN THE PROVISION ANDFINANCE OF HIGHER EDUCATION'

by

W. Lee Hansen and Burton A. Weisbrod

1, Based on material in chapters 4 and 6 in W, Lee Hansen and Burton A. Weisbrod, !Edits, Costs anclance of Hi hetLittpatIon, Chicago, Markham Publishing Co 1969, See also W. Lee Hansen and Burton A, Weisbrod, "The Distribution of Costs andDirect Benefits of Public Higher Educatiom The Case of California", journal f uman Resources, Spring 1960, pp, 116-191.

INTRODUCTION

Who should be eligible for public higher education? Should those young people who are not eligible- or, if eligible, are unable or unwilling to go to college - bo deprived of the public subsidies obtainedby the college goers? What can be said about the actual distribution of public subsidies for highereducation - that is, who actually receives them? And who payb or them? These and related questionsare explored in this paper, which is addressed to the subject of equity in the provision and financing ofhigher education. First, some conceptual issues are treated, and then a newly-available body of datais analysed with the objective of determining how the benefits and costs of public higher education areactually shared in our most populous state, California.

EQUITY AND EFFICIENCY: CONCEPTUAL ISSUES

How should public higher education be financed? There are actually two separatable questions: one,who should bear the costs of public higher education; two, how the portion of costs that is borne bystudents should be paid. More precisely, the question of who should pay involves determining the shareof costs to be paid by students versus taxpayers'. The question of how. students should pay relatesdirectly to the tuition issue, but "the tuition" is not a simple concept. Should tuition be the same for allstudents? Whatever the level or levels of tuition, should it be paid at the time the education is received,or later? Should the level of tuition be determined at the time the education is received, or should theamount be contingent on future benefits?

The nature of these choices will be described more fully below. While our primary concern in thispaper is with equity, we recognize that sound public policy should also strive for efficiency in «he useof resources. Thus, we begin witn a discussion of what we mean by "efficient" and "equitable" solutionsto educational finance questions.

By "economic efficiency" we mean the degree of success of higher education in producing outputs(trained students, for example) that are more valuable than the resources used up in the process ofproduction. In the economy at large, the value of output is generally measured by what people arewilling to pay for it, and, so, as a first approximation, the value of college education may be measuredby the increased salaries that employers are willing to pay for workers who are college educated ratherthan only high school educated. Efficiency, in the present context, can thus be thought of in terms ofthe amount by which national income (or Gross National Product) is raised by higher education2.

But, whichpeople receive this increased Income? And who pays the costs of the resources - teachers,classrooms, laboratories, etc. - that are required to produce the increased income? In other words,how "fairly" are the additional income and the costs of public higher education shared? This is the issueof equity.

The distinction between efficiency and equity is essential if we are to come to grips intelligentlywith difficult issues of public policy. Higher education may be found to be efficient in raising incomes,but the method of financing hther education might be regarded as inequitable. By contrast, it may befelt that higher education is being financed equitably, but that it is really not an efficient way to useresources - there being better ways to increase poopte's real incomes (such as by devoting more re-sources to improving technology). Of course, there are intermediate positions, in which various degreesof inefficiency and inequity are adjudged to exist,

1, There is, of course, the question of how the taxpayers portion of the costs is to be shared among various groups, but we do

not deal with this matter,2, But this is only a first approximation of the full value of college education, because it disregards benefits that arise in ways

other than through the Job market, We return to this point below, On the other hand, it disregards the fact that the increased salariesreflect not only the effects of schooling but also of the generally greater ability of those students who have opted for more schooling,

205

149

Debate over issues in higher education finance can only be fruitful if there is a recognition of when,and to what extent, the dispute centres on factual matters of efficiency, and when it centres on valuejudgments regarding the fairness of the distribution of benefits and costs, This is not to deny, however,that both classes of issues are difficult to resolve, for the factual data relevant to assessment of effi-ciency are diffioult to find, as is consensus on what should be regarded as equitable,

The sooial objectives of ei:ciency and equity are in fact quite likely to conflict, thereby complicatingthe issue, Consideration of efficiency might suggest that higher education should be provided to someyoung people but not to all; implicit is the widely held assumption that not everyone oan benefit signifi-cantly from higher education, But there is still the equity question: it is "fair" for some youngstersto receive public subsidies while others do not? An efficient allocation of resources can be inequitable,

And, an equitable allocation of resources can be inefficient, lf, for example, every youngster werenot only offered the opportunity to go to college for four years, but were required to go, then all college-age people would roceive a similar public subsidy, But if this is more equitable it is doubtless lessefficient, for not everyone is likely to benefit enough to cover the oosts of resources required to educatethem, The conflict between equity and economic efficiency in higher education planning appears to bea genuine one; we do not attempt to resolve it here, but rather foous on the iseue of equity itself,

Throughout this paper our attention is directed primarily to decision-making in the public sector,This orientation is somewhat artificial, The fact that there exists a private s well as a public sectorin higher education means that success in devising an efficient and equitable finance system for publichigher education does not assure either efficiency or equity for the higher education system as a whole,although our analysis of efficiency and equity issues in the financing of public higher education isapplicable to private as well as public higher education, The question of what separate and distinct rolesought to be fulfilled by the public and private sectora in higher education is an important one, but scantattention has been given to it, To have considered carefully the role of the private colleges, however,would have further complicated an already knotty matter,

Efficient Pricing

Before embarking on our detailed investigation of equity, we turn to a brief analysis of some impli-cations of seeking efficient pricIng of higher education, As already noted, both kinds of considerationsare relevant to the evaluation of alternative methods of financing public higher education,

The cost of a college education to a student and his family - apart from the income foregone - can'.n analysed in two parts, One is what can be termed the "price" of the education - the tuition charge,the books and supplies, and so forth, The second is the "ease of financing" the price - that is, theavailability and terms of loan funds and scholarships,

The level of the price of college education, and the ease of financing it, are jointly relevant toindividuals' decisions, An apparently high tuition rate may be quit', inanageable if grants or scholarshipsare widely available or if loans can be obtained at sufficiently low interest rates, Similarly, even atot61 failure of scholarship programmes and capital markets to provide financing assistance can turn outto be inconsequential if the total price of education (including foregone income) is sufficiently low, Thus,there woid,1 seem to be trade-off possibilities between the price of education and the means of financingit - combinations among which any particular individual would be indifferent,

But considerations of public policy dictate that we go beyond an analysis of any individual's prefer-ences to take account of all the resources used up in the process of satisfying those preferences, Thus,we are led to consider the questions of what is a socially efficient prioe of education, as well as what isa socially efficient set of finance terms, including an interest rate,

Economic efficiency may be said to exist in a market when the price of the good or service is equatedwith the marginal opportunity oost (value of the best alternative use) of the resources used to produce it,

igh

and both are equated with the benefits from an additional unit of the good, rhus, given the distributionof income, the preferenoes of all individuals in society, and the technological production possibilities,the efficient price for any given unit of production (e. g, man-year) of higher education is the price whichis equal to the marginal net social cost of providing that education and the marginal benefit received bythe student, By net oast we mean the marginal oost of pruduotion Wails any margMal "external" benefits,that is benefits that are not captured by the individuals whose education produced theml, To the extentthat suoh external benefits occur, the efficient price to oluago students would be below the marginaloost of producing the education servioee

This view of pricing clearly implies that society (taxpayers in general) should subsidize higher edu-oation as a matter of efficiency. Since some external benefits may be realized within local areas whileothers may be distributed more broadly, all levels of government - federal, state, and local - wouldpresumably share in the costs. Insofar as the bulk of externalities accrue at the national level, in partbecause of population migration, this would argue for a reallooation of public financing of higher edu-cation away from state and local governments and to the federal government,

Public subsidies clan take.. a variety of forms. In addition to "low" tuition rates, there are low-costloans, income tax 'credits or deductions to parents, and outright clash grants to students, all of whichcan be equivalent to a tuition reduction. Any of these forms, and no doubt others as well, could be usedto produce the desired public: subsidy and, in turn, result in an effioient "price". The oholoe among themrests largely on an equity consideration - that is, the extent to whioh persons not in "need" wouldbenefit3.

There are some individuals who may be "qualified"4 for college but who will not attend 'collegebecause the combinations of available price and interest charges are "excessive" relative to their finan-cial situation and to the strength of their desire to attend, The willingness to incur these oosts isconditioned by factors including family income and wealth, family size, and parental health, Yet thereappears to be a social consensus that these factors ought not to bar college attcndance, so that "needy"individuals with the ability and motivation to benefit from college should go.

If compulsion Js to be avoided, these barriers to college attendance could be offset in three generalways: a) incomes of such students and their families might be supplemented; and/or b) the price ofcollege education for them could be reduced; and/or o) the interest rate applicable to their borrowingfor college could be reduced.

One might argue that the judgment that a student "should" go tc college, even though family cir-cumstances would lead him not to go, represents an implicit social decision that his family's inoome is"too low", Thus, an increase in family income would seem to be called for. If the objective, however,is to make it possible for this student to attend college at a minimum cost to others, then the approachof giving to needy students cash transfers that are not restrioted as to use, is likely to be inefficient Ivery substantial transfers might be required before any of the additional money would be used for thestudent's higher education. A possible variant is to restrict the use of cash grants to higher education.But this alternative may be difficult to implement, since as a praotioal matter there are no means forpreventing some of the grant money from going to families - even some of them with very low incomes -whose children would have gone to college anyway and who now, having received the grant, will be able

1, At me conceptual level, the possibility of external costs as well as benefits should be considered, It is not generally argued,

however, that such costs are notable, if, indeed, they occur at all in higher education,2, It is difficult to estimote marginal costs, but it might insolubly be assumed that iong-run marginal cost can be approximated

by average instructional plus capital costs,3, For further discussion of this issue in the context of income redhtributional programmes see I3,A, Weisbrod (JEC paper, vertical

efficiency),4, It seems cleat that there is considerable arbitrariness in deoiding who is "qualified" to benefit from a college education,

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151

to inorease their expenditures on other goods and services, Grants to suoh families are not neoessarilyundesirable, but the point is that grants may not be required to aohiwe eduoational objectives, howeverjustified they may be from the point of view of a more general anti-poverty effort.

Consider now the alternatives of reduoing the Woe and/or interest rate for the "needy". If, tobegin with, the price and interest rate were set at levels that were eoonomioally offiolent - in terms ofthe oosts involved, as disoussed in the preoeding seotion - then further reduotions would saorifioesome allooative efficienoy in order to bring about effeots that were deemed more equitable. Such a trade-off of efficiency for equity is by no means unique to higher education, nor is it necessarily undesirable.

In practioe, each of the alternatives is bound to fall short of fully realizing equity objeotives, Sub-sidies, whether in the form of oash, tuition rate reduotions, or reduotions in interest rates, are oertainto go to some persons other than those whom "sooiety" specifioally wishes to assist, since the "needy"and "deserving" are frequently difficult to identify. Thus, subsidies go, at least to some extent, tothe "wrong" people - with taxpayers, some of whom are themselves worthy of help, paying the cost.

Some perspeotives on the dimensions of need can be obtained by a theoretioal disaggregation of thepopulation into several different groups, Group I includes those students (and their families) who arewilling and able to pay at least the full long-run marginal cost (which we suggested above might beapproximated by average instructimal plus capital cost) net of estimated external benefits, and the fullmarket interest rate. A portion of this group, while willing to pay these costs, can do so only byincurring some "hardship", Group II includes those who are willing and able to pay some lower, positiveprice and interest rate, and some fraotion of this group could pay these amounts only with some hardship.Finally, Group III includes those people who would need bribes to cause them to attend college, beingunwilling to attend at any combination of a positive price and positive interest rate, All three groups aredefined to include only those deemed "eligible" - in terms of aptitude and motivation - to attend college.

One of the implications of the structuring of these three groups is that the amount of subsidy requiredto cause an individual to attend college is a continuous variable with a wide range of values. Some stu-dents will require very subatantial subsidies and others none at all in order to provide full equality ofopportunity in higher education.

Identifying those who are deserving of additional subsidies to enable them to go to college or to gowithout undue hardship is a most difficult task. Assume, however, that the "need" for higher educationsubsidies can be estimated in a satisfactory, if rough, manner, perhaps applying the standards used instudent financial aid analyses. The perplexing question then is who should pay for these equity-basedsubsidies? Utilizing taxpayers in general as a source of revenue, while havthg merit, does imply thatany sum of money that students and their families "cannot afford" to pay, can be paid by, and should bepaid by taxpayers. But when it is borne in mind that "taxpayers in general" include many quite lowincome taxpayers, it becomes olear that a shifting of the financial burden from students and their familiesto taxpayers involves, to some extent, a shift of the burden to families whose incomes and ability to paymay be less than the ability to pay on the part of students and their parents,

This raises a more fundamental issue of the meaning of "ability to pay", Just as standards havebeen established for determining how much a family can "afford" to pay for higher eduoation, so mightstandards be established to determine how much a family could "afford" to pay in taxes, If such a studywere done, it might well conclude that families of given size, given needs, and with incomes below somespecified amount, could not afford to pay any taxes at all; nevertheless, we suspeot that many suchfamilies are, in fact, actually paying taxes - and would be required to pay even more taxes if Mate sup-port for higher education were increase&

Another possible source of subsidy fads for the needy is otller oollege students and their parents.We noted above that there ars some families, partioularly in Group I, who are able and willing to paymore than the efficient prioe of eduoation, If they were oharged a higher prioe, the subsidies requiredfor needy students could be obtained outside the tax system. This would amount to the use of classic)

price discrimination, to charge what the traffic will bear, One might think of the resulting schedule ofcharges as reflecting a sliding-scale college payment plan, with the possibility of negative charges forthe most needy. 1

On the assumption that a choice oan be made regarding the most appropriate subsidy device forachieving greater equity, there is still a larger issue concerning the propriety of limiting subsidies tothose who choose college rather than some other means for enhaaoing individual and social well-being.For the many young people not deemed qualified for college or not interested in attending college underany reasonable pricing conditions, there is a variety of other methods by whioh they ean enhance theirIncomes and future satisfaction, and otherwise become effective citizens, Job training and investmentsin small businesses are only two substitutes to college-going. Whether from the standpoint of achievingequity or efficiency in resource allocation, it would be highly desirable to make these and perhaps otheralternatives available to those young people who do not opt for college. A broadened subsidy programmemight well be more costly, But it would at the same time do much to provide greater equality of oppor-tunity for all young people, not merely for college studants.

The relevance of the proposal for broadening the subsidy base will become clearer as we turn to theemp:rioal results of our investigation of how the benefits and costs of public higher education are sharedin California, We see that a large percentage of all young people receive no public) subsidy at all throughthe public higher education system, while a small percentage receives very substantial public, out-sidles,

1, Michigan State University has been experimenting with such a plan, though in a quite restricted form, The sliding-scaleapptoach is also implicit in cases where the size of scholarships is a function of "need",

II

THE DISTRIBUTION OF COSTS AND DIRECT BENEFITS OF PUBLICMILER EDUCATION: THE CASE OF CtLIFORNIA

The public higher education system in the United States provides - or, at least, offers - a publicsubsidy to young people of college age. The extent to which the young people actually receive th e. sub-sidies depends on a) whether they can qualify for admission, b) whether they avail themselves of theopportunity to attend, and, if they do, c) what quantity and quality of education they receive. As a result,the arr.Junt of subsidy received through the public financing of higher education varies greatly from oneperson to another. Our objective in the remainder of this paper is to estimate a) the amounts of sub-sidies received through higher education, b) the variation in subsidies received by students depeadingupon the amount of schooling and the kind of schooling they obtain, and c) the extent to which these sub-sidies are received in different amounts by students whose families are at different socio-economiclevels.1

Attention is restricted to undergraduate education, and the data used are for public education inCalifornia, While higher educational systems differ among states, it would appear that the results forCalifornia are broadly characteristic of those for a number of other states.

A knowledge of the magnitude and distribution of subsidies or direct benefits provided through publichigher education, or indeed through any public programme, is important for what it suggests as toappropriate pricing, tax, and expenditure policy, By "appropriate we mean policies that will be effi-cient in the sense of doing the most to raise output, and at the same time equitable in the sense of doingthe most to achieve society's distribution goals, such as providing greater equality of opportunity foryoung people. We can illustrate some of the possibilities, For those "eligible for higher education,uniform subsidies may provide a "windfall" to the more financially able, while doing little to facilitatecollege attendance by the less well-off, This might argue for some kind of flexible pricing system inhigher education, though much the same effect might be achieved less directly through the tax system.For those not eligible for public higher education, the provision of other kinds of subsidies or direct-benefit programmes may not only yield substantial benefits to others but also help to achieve greaterequality - of both educational opportunity and of opportunity in general,

pubsilents Qan fløive

The amounts of public higher education subsidies that college students can and do receive are thedifference between tuition and the costs - instructional and capital - of providing instruction to themThe size of this difference for any student depends on the number of years of instruction received, andthe subsidy per year of schooling. The latter, in turn, depends essentially on the costs of the particularcollege, and on its price (primarily tuition),

1, Little effort seems to have been given to this subject, For one intrcesting and perceptive foray, see Christopher Jencks,"Social Stratification and Mass Higher Education", Ward Etlukation Review, Spring 1968,

1211

1154

In 1965 the public subsidy provided through higher education in California ranged from $720 for ayear at a Junior College to $1,350 and $1,450 for a year in the lower division (first two years) at aCalifornia State College and at the University of California, respectively. But the one-year subsidiestell only a portion pf the subsidy story, for, while some students may attend a publio college for only ayear or even less, others attend for four years or more, And not only do those who attend for longerperiods receive larger subsidies for that reason alone, Iwt also because the subsidies increase as stu-dents progress to the upper division levels. For California, students who complete a two-year JuniorCollege programme receive an average stibsidy totalling $1, 440 , while those completing a baccalaureateprogramme at a State College receive four times as large a subsidy - $5,800 - and graduates from aUniversity of California campus receive a four-year subsidy of more than $7,100. The actual amountsof subsidies vary, depending upon patterns of transfer among these three segments of the Californiapublic higher eduoation system.

The proportions of students entering eacil segment of higher education who actually complete it varyconsiderably, from about 60% at the University, to 55% at the State Colleges, and to 30% at the JuniorColleges. But even this is deceptive, since many eligible students do not avail themselves of any publichigher education. Some prefer to enter the work force, others enter the military service, and manyfemales marry and do not continue their schooling, Still others enrol in private institutions of highereducation in California, while another but smaller group seeks higher education outside of California,

Of those who do enrol in public higher education in California, the proportions eligible for eachsegment who actually enrol in that segment are oftenvery low, Por example, of the 19% of high schoolstudents eligible for the University of California in 1965, only 5% planned to enrol at the University;another 4% planned on going to State Colleges, 5% to Junior Colleges, 3% to other institutions, and 2%planned no further education, Of those 17% eligible for State Colleges (but not for the University), 2%planned to enrol at a State College, 8% at the Junior Colleges, and 4% did not plan to enrol at all. Andwith respect to the Junior Colleges, for which all students ale eligible, only some 30% of high schoolgraduates planned to enrol; this constituted one half of the 64% of high school graduates who were noteligible (on the basis of scholastic performance in high school) for either the University or a State College,Thus, whatever their reasons, many high school students enrol at public institutions of higher eduoationin California which provide subsidies smaller than those for which they are eligible.

Just as the amount of public subsidy varies among the three segments of the California higher edu-cation system, so do the attrition rates, Students who enter a Junior College not only reueive thesmallest subsidy per year, but they are most likely to remain in school for only a short time, Bycontrast, students who enter the University of California receive a far greater subsidy per year and aremost likely to receive that subsidy for four years, until graduation. The high attrition rate at the JuniorCollege level reflects in part the fact that a number of its programmes require only ovte year of schooling,The rate of attrition at the State Colleges is somewhat lower, and attrition at the University of Californiais the lowest, largely as a result of its greater selectivity in udmissions.1 Its first-year attrition rate -15% - seems rather high, but the four-year completion rate of 55% is within the range for most othercomparable four-year institutions, However, an additional 3% of the initial entrants to the Universityof California completed their work at a State College, and some others undoubtedly graduated fromcolleges nutside the California system of public higher education.

Distribution of Amounts of Subsidies

We have constructed a rough distribution of the percentage of an age cohort of high school graduateswho receive different amounts of public subsidies for higher education, utilizing data on instructionaland capital costs, transfer patterns among the three systems, and attrition rates. This information issummarized in Table 1, The rather startling conclusion is that while a small proportion - 9% - receivesrather large subsidies, exceeding $5,000, more than half of California's young people receive under

1, For additional details see e ancluotition o oitt Chapter 4,

it5

Table 1, ESTIMATED DISTRIBUTION OF PUBLIC SUBSIDIES FORHIGHER EDUCATION, BASED ON AMOUNT RECEIVED

DURING PERIOD ENROLLED

AMOUNT OFSUBSIDY ($)

0

1 - 749750 - 1,999

2,000 - 3,4993,500 - 4,9995,000 - 6,4996,500 .

PERCENTAGE OF

PERSONS RECEIVING

411430

3

3

6

3

100

$750 in total subsidy for higher education. And a substantial fraction - 41% - receive no subsidy atall. This group is divided t.etween those who obtain no higher education whatsoever - almost 80% -and those who plan to attend private colleges within California or colleges outside the state - about 201

In short, there is a highly unequal distribution in the amounts of public subsidies actually received,even though California prides itself on the wide access to higher education it provides and the highenrolment ratios which are presumably a reflection of this. Moreover, there is little reason to believethat the distribution of public subsidies through higher education is less unequal in other states than it isin California. No state has as widely accessible aJunior College system as does California; thus, otherstates probably have larger proportions of young people who obtain little or no college education.

Distribution of Subsidies by Family Income

What can be said about the distribution of subsidies provided through higher education when measuredagainst students' family income levels? While this is a difficult question to answer with the availabledata, we have tried to shed light on it.

To begin with, it is useful to examine the patterns of college-going by level of family income. Theseare shown in Table 2, where columns (3)-(6) show the family income distributions for all Californiapublic college students in 1964; column (2) shows the Income distribution for families without childrenin California public higher education, and column (1) shows the distribution for all California families.

The distributions 13;; family income clearly differ among the groups shown. Median family incomes(see bottom row of table) are highest for parents of university students, followed by State College stu-dent families and Junior College student families. Lowest of all is the median for all families withoutchildren in the California system. (This is heavily weighted with elderly and, on average, low incomefamilies. ) These patterns ftre about what one might expect and, in general, conform to the patternsshown in other surveys,' Thus we conclude that access to subsidies is positively related to levels of

1. For example, see C,e Wisconsin data in L.), tins,aft? *

A, P. Abell, and D.R. Stucki, Co ts of AttenOanoe and Income of Madison, Office of Institutional Studies, January 1961; I. M. Soyak,

aukee_Students. 1064-196S Academic,,

Lino, A. P. Abell, and R, Hammes, COM of Attejgo cein Year, Office of Institutional Studies, May 1066,

4eiA.P. Abell, and Li. tins,na, Office of Institutional Studies, March 1961: and L,I.

iVersity of Wisconsin ter St dell kcadejn

1156

Table 2, DISTRIBUTIONS OF FAMILIES BY INCOME LEVEL AND TYPE OF COLLEGEOR UNIVERSITY , CALIFORNIA, 1964

(In Pernentag

INCOME CIA SS

$

ALL FA MILIES

FAMILIES WITHOUTCHILDREN IN

CALIFORNIA PUBLICHIGHER EDUCATION

FAMILIES WITH CHILDREN IN CALIFORNIAPUBLIC HIGHER EDUCATION

TOTAL 1C SC UC

(1) (2) (3) (4) (5) (6)

0 - 3,999 16. 1 17. 0 6. 6 8. 1 4. 1 5. 0

4,000 - 5,999 14. 8 14. 9 13. 0 15. 9 10. 2 7. 56,000 - 7,999 18. 9 19. 0 17. 6 19. 6 17. 0 11. 1

8,000 - 9,999 18. 1 18. 3 16. 4 16. 9 17. 2 13. 1

10,000 - 11,999 12. 4 12. 1 15.8 14. 4 19. 9 13. 3

12,000 - 13,999 7. 4 7. 3 8.8 17. 2 10.8 11.314,000 - 19,999 7. 9 7. 5 13.0 11. 1 13.0 20.320,000 - 24,999 1. 8 1. 6 3. 4 2. 6 3. 3 6. 6

25,000 + 2. 6 2. 3 5. 4 4. 2 4. 5 11. 8

Total 100. 0 100. 0 100. 0 100. 0 100. 0 100. 0

Median Income $8,000 $7,900 $9,560 $8,800 $10,000 $12,000

NOTE: JC (Junior Colleges); SC (State Colleges); UC (University of California),

SOURCE: Column (1) - Letter from Office of Legislative Analyst, California Legislature, in Tuition for California's Public Institutionsof Higher Education, Joint Committee on Higher Education, Hearings, 13th October, 16th October, 1961; seeTab T, Table 1,

Column (2) - Percentage distribution of Column (2), calculated by authors.Column (3) - Weighted average of Columns (4), (6) and (6).

Columns (4),(6),(6) - Edward Sander, and Hans Palmer, The Financial Barrier to Higher gduoation in California (Clarementt PomonaCollege, 1966), Table M, p, 21, which relates to distribution of parent-supported students only.

family income, with the highest single-year subsidy going to UC students (and their families) who al-ready have the highest median family incomes ($12,000).1

We can present some crude figures to illustrate the association of family income and subsidies re-ceived, by comparing median family incomes for the groups shown in Table 2 with the amounts of thesubsidies going to each of these groups. Table 3 presents our estimates of these data. Median incomeof families of various types is shown in line 1, the one-year subsidy received is given in line 2a, andthe subsidy as a percentage of family income is presented in line MI Because .students first enrollingat each type of institution do not remain in college equally long, the average number of years they areenrolled is also shown, in line 3, The total subsidy received is shown in line 4a, and the percentage offamily income that the subsidy constitutes is in line 4b. Because students transfer among the threehigher education systems, the average subsidy is not simply the product of the average subsidy in aparticular system and the average number of years of schooling obtained by students who begin theirschooling in that system. As indicated by line 2b, the values of the single year subsidies vary from

1. Were we to relate the data shown in Table 2 to the data on subsidies received over the entire college stay, the differences inthe subsidies received would be accentuated, The reason is that University of California students are more likely to complete fouryears than are State College students, and the latter Are more likely to complete four years than the vast bulk of the students who beginat Junior Colleges,

A 214f'

157

Table 3. AVERAGE FAMILY INCOMES AND AVERAGE HIGHER EDUCATION SUBSUMES RECEIVEDBY FAMILIES, BY TYPE OF INSTITUTION CHILDREN ATTEND, CAUFORNIA, 1964

ALL FAMILIES

FAMILIES WITHOUTCHILDREN IN

CALIFORNIA PUBLIC

HIGHER EDUCATION

FAMILIES WITH CHILDREN IN CALIFORNIA

PUBLIC HIGHER EDUCATION

TOTAL JC SC IJC

(1) (2) (3) (4) (5) (6)

Average family income (i) 8,000 7,900 9,560 8,800 10,000 12,000

Average higher education sub-sidy per year (ii)

a) Amount in dollars - 0 880 720 1,400 1,700

b) Per cent of line 1 - 0 9 8 14 13

Average number of years ofhigher education completed n. a. n. a. n. a. 1.2 2,6 2.8

Average total higher educationsubsidy

a) Amount in dollars - 0 1,700 1,050 3,810 4,870

b) Per cent of line 1 - 0 18 12 31 41

(1) Median incomes from Table 2.(ii) Average subsidies are based on the distribution of enrolment by year of school and on distribution of enrolment by type of institution.

zero per cent of family income for those without children in public colleges and universities (some ofthese people may have children in private colleges or in public colleges not in California), to 14% offamily income for those families with State College students.

The average overall subsidy is equal to 9% of current money income for all parents of publicly-enrolled college students (line 2b, column 3), but the subsidy climbs to 18% of family income when wetake account of the number of years that the educational subsidy is received (line 4b, column 3).Because, as noted before, the amount of schooling received differs, the average total subsidies (line 4a)rise far more sharply than the single-year subsidies (line 2a), as we contrast the families with childrenenrolled in California Junior Colleges, State Colleges, and University. These patterns of subsidiesraise serious questions about the equity of the currert system for financing public higher edu-cation in California.

At the same time, however, the distributions of students by parental income (as shown by each ofthe columns in Table 2) are so wide for each type of system - University of California, State College,and Junior College - that any strong conclusions about the "class-servine nature of the entire systemof higher education in California cannot be drawn. While there is a tendency for the higher subsidyschools to draw a higher-income clientele, the overlap of the distributions is still very substantial.

Some added light can be thrown on the equity issue by a restructuring of recent data presented bythe California Co-ordinating Council for Higher Education.1 The data from several of its tables have been

1, Co-ordinating Council for Highe: Education, State of California, calAasillocekonms, 61-18 (Second Revision)31st October, 1961, Table 1-2, p, 1-91 Table 1-3, p, 1-1A and Appendix Table 13-3,

215

158

combined to show how eligibility and plans for higher education enrolment vary systematically withincome,

We see in Table 4 that under 20% of high school graduates qualify for the substantial Universitysubsidies; this is a product of the academic entry requirements, Even more striking is the fact thatthe percentage of all students qualifying for the University of California (column 1) rises quite dramat-ically by family income level - from about 10% in the lowest income bracket (under $4,000) to 40% inthe highest (over $25,000). Thus the correlation between high school achievement and family income -and all that it reflects - is startling indeed. This pattern persists as we widen our view to include thoseeligible for both the University and those who are eligible for State Colleges (column 2). But a closeexamination of the differences between the two columns shows that the percentage of those eligible onlyfor the State *lege system is roughly constant with respect to income level; thus, University eligibilityrequirements account largely for the unequal distribution of opportunity.

Table 4. DISTRIBUTION OF HIGH SCHOOL GRADUATES BY ELIGIBILITY FOR PUBLIC HIGHEREDUCATION IN CALIFORNIA, BY TYPE OF EDUCATION AND FAMILY INCOME

(In percentage)

FAMILY INCOME

PERCENTAGE DISTRIBUTION OP HIGH SCHOOL

GRADUATES BY ELIGIBILITi FOR

UNIVERSITY OF CALIFORNIAUNIVERSITY OF CALIFORNIA

AND STATE COLLEGES

0 - 3,999 10. 7 28. 04,000 - 5,999 11. 5 26. 36,000 - 7,999 11. 9 30. 58,000 - 9,999 16. 2 33. 2

10,000 - 12,499 19. 4 37. 112,500 - 14,999 22. 5 39. 815,000 - 17,499 27. 9 45. 417,500 - 19,999 29. 5 45. 120,000 - 24,999 33. 3 46.125,000 + 40. 1 54. 3Not reported 13. 3 28. 0

All 19. 6 36, 3

NOTE: Excluded from the sample of 8,162 were 302 students planning vocational training, 38 non-respondents on enrolment plans, and20 for whom eligibility was indeterminate,

SOURCE: Based on data from CCHE, FittancialAtsionce_Pi'groms, 61-13, (Second Revision) 31st October, 1967, Table 1-2, p, I-91Table I-3, p, 1-10: and Appendix Table 13.3

The extent to which family income influences the likelihood that a student who is eligible for a highsubsidy school will go to it is indicated in Table 5. For the University (column 1) a larger fraction ofupper than lower income students plan to attend; the same holds for the combined University-StateCollege system group (column 2); and the pattern continues - though in somewhat muted famhion - whenwe consider all high school graduates icolumn 3). Actually, these results are somewhat deceptive sincethose eligible for a "higher" system can also attend a "lower" system. Indeed, when we compare thepercentage of University eligible students planning to attend one of the three public systems, we find thatthe proportion is fairly constant with respect to family income, at about 70-75% (these data are notshown in the acoompanying tables), Much the same kind of pattern emerges for both the University and

216

159

2able 5. COLLEGE ATTENDANCE PLANS OF CALIFORNIA HIGH SCHOOL GRADUATES,BY FAMILY INCOME AND HIGHER EDUCATION SEGMENT, 1966

(In percentage)

FAMILY INCOME LEVEL

($)

PER CENT OF UCELIGIBLES PLANNING

TO ATTEND UC

PER CENT OF UC-SCELIGIBLES MANNINGTO ATTEND EITHER

UC OR SC

PER CENT OF ALL CALIFORNIA

HIGH SCHOOL GRADUATESPLANNING TO ENROL IN

UC, SC OR ,IC

'0 - 3,999 30. 4 22, 5 53,14,000 - 5,999 26, 1 29. 7 56.16,000 - 7,999 23. 4 28. 1 56.38,000 - 9,999 21, 5 36. 5 60. 0

10,000 - 12,499 25. 3 32. 6 62.012,500 - 14,999 26. 2 37. 5 64. 615,000 - 17,499 26. 9 32. 1 63.417,500 - 19,999 33. 3 45. 7 64.220,000 - 24,999 45, 4 52. 0 . 68. 225,000 + 46. 7 47.8 57.8No response 30. 5 30. 1 47. 9

SOURCE: Same as Table 4,

State College eligibles who plan to undertake higher rducation, The point, however, is that enrolmentin a lower system - often dictated by family income considerations - hnplies a reduced level of sub-sidies.

Who Pays the Taxes?

Having shown the extent to which families in different income groups are awarded subsidies throughthe fiscal system by virtue of the provision of higher education, we turn now to the question of howthese subsidies are financed, Specifically, we estimate distributions of state and local taxes paid byfamilies at each income level, The objective is to provide a basis for comparing the subsidies receivedwith the tax payments made, Such information is essential in assessing the equity of the current methodsof financing higher education in the State of California.

Our approach is to estimate the incidence of the most important state and local taxes by familyincome level, so as to note the absolute amount of taxes paid at each income level. We can then comparethis amount with the subsidy received and note any differences, But we still have no real way of deter-mining how much of whatever taxes are paid reflect support for higher education, as against the manyother services provided by state and local governments.

The average amount of taxes paid at each income level as well as the effective tax rate, forCalifornia state taxes alone, and for state and local taxes combined, is shown in Table 6, The mostimportant finding is that while the state tax structure (column 2) seems to be somewhat progressive -that is, the effective tax rate rises with income - except in the lowest income classes, the combinedstate and local tax structure (column 4) is regressive below $8,000 and is essentially proportional abovethat level,1

1, The recent, 1967, changes in the California state income tax structure have inoreased, but only slightly, the overall props-sivity of the state tax structure,

1,60

Table 6. ESTIMATED TAX BURDENS BY INCOME CLASS, CALIFORNIA, 1965

ADJUSTED GROSSINCOME CLASS

($)

STATE TAXES

ONLY PER

FAMILY a)

($)

EFFECTIVE

STATE TAXRATE b)

(%)

STATE ANDLOCAL TAXESPER FAMILY c)

($)

EFFECTIVE

STATE AND LOCALTAX RATE b)

(%)

(1) (2) (3) (4)

0 - 3,999 104 5.2 474 23.74,000 - 5,999 132 2.6 527 10,5

6,000 - 7,999 161 2.3 576 8.28,000 - 9,969 221 2.4 696 7.7

10,000 - 11,999 301 2.7 833 7.612,000 13,999 389 3.0 984 7.614,000 - 19,999 539 3.2 1,228 7.220,000 - 24,999 865 3.8 1,758 7.8

25,000 4. 2,767 5.5 4,093 8.2

SOURCES: Personal income, sales, cigarette and beverage taxes by income level were obtained from Letter from Office of Legislativr.

Analyst, State of California in Tuition for California's Public Institutions of Higher Education, Joint Committee on Higher

Education, Hearings, 13th and 16th October, 19611 see Tab, T, Table 1, State gasoline taxes and local property taxes were

based on itemised tax deductions reported on state income tax returns, 1965, and summarized in Franchise Tax Board,

Annual ports, j965 and 1966, Table 13, Local sales taxes were assumed to be distributed in the same manner as state

sales taxes above, Since local sales tax revenues in 1965 equalled one third of state sales tax revenues, this factor was

applied to the estimated amount of state sales taxes in each income level,a) Personal income, state sales, cigarette, and alcoholic beverage taxes only.b) Taxes as a per cent of estimated mean income of each income class. The mean of the highest income interval was

arbitrarily assumed to be $50, 000.c) State taxes include personal income, sales, cigarette, alcoholic beverage, and gasoline taxes. Local taxes include

local sales and property taxes.

We return now to the major task of this section - to compare the taxes paid with the subsidies re-ceived by families with children enrolled in college, so that we can observe the extent to which broadgroups of families do or do not receive net subsidies through higher education. In making such com-parisons we once again remind the reader that this involves comparing all taxes with benefits receivedfrom higher education alone. As shown by Table 7s the annual value of higher education subsidles (line2) received by a family with a single child enrolled in a public college exceeds the total amount of allstate and local taxes they pay (line 3), by rather substantial amounts. On an overall basis the averagehigher education subsidy is $880 per year (line 2 column 3), in contrast to total state and local taxespaid of $740 (line 3, column 3); this results in an annual net transfer of $140 from all taxpayers toparents of each college student, But this average conceals wide differences by type of college.

For families with a child at one of the state Colleges or one of the University campuses the nettransfers range from $630 to $790 per year, Meanwhile, families without children or with children notenrolled in public institutions of higher education receive no subsidy whatsoever, while they pay anaverage of $650 in state and local taxes, This is not to suggest that such families shbuld pay no stateand local taxeb for some may have benefited in the pasts others may benefit in the futures and stillothers may have opted for more expensive non-public California higher education, Moreover state andlocal taxes finance public services other than higher education. In any eases as is evident from a com-pute( a of line 4 and line ls the current method of financing public higher education leads to a redistri-bution of income from lower to higher income families; indeed, there is very substantial progressivityIn the resulting pattern of transfers,

2k8.

161%

Table 7, AVERAGE wAMTLY INCOMES, AVERAGE HIGHER EDUCATION SUBSIDIESRECEIVED, AND AVERAGE STATE AND LOCAL TAXES PAID BY FAMILIES,

BY TYPE OF INSTITUTION CHILDREN ATTEND IN CALIFORNIA, 1064

ALL

FAMILIES

FAMILIES

WITHOUTCHILDREN INCALIFORNIA

P U13LIC

HIGHER

EDUCATION

1.010FAMILIES WITH

CHILDREN IN

CALIFORNIA PUBLICHIGHER EDUCATION

TOTAL IC SC UC

(1) (2) (3) (4) (6) co

1. Average family income a)

2. Average higher educationsubsidy per year b)

3. Averagea total state and localtaxes pLid c)

4. Net transfer (line 2 - line 3)

8,000

-

620

-

7,900

0

650

-650

9,560

880

740

+140

8,800

720

680

+40

10,000

1,400

770

+630

12,000

1,700

910

+790

a) From Table 2.b) From Table 3.c) Total state and local tax rates from Table 9 were applied to the median incomes for families in each column.

219

CONCLUSION

Public policy regarding higher education must consider a number of factors among which the eco-nomic efficiency of expenditures on higher education and the distributional equity of the public supportfor higher education are surely prominent, After a brief analysis of the economic efficiency issue, thispaper turned to its primary objective - an empirical investigation of the distributional effects of publichigher education in our most populous state, California,

The general nature of the redistributive effects of the current method of financing public highereducation in California is clear, Some low income persons have benefited handsomely from the avail-ability of publicly-subsidized higher education, But on the whole, the effect of these subsidies is topromote greater rather than less inequality among people of various social and economic backgrounds,by making available substantial subsidies that lower income families are either not eligible for or cannotmako use of because of other conditions and constraints associated with their income position,

ro overcome the effects of the present system would require a substantial overhaul of tho pricingsystem in public higher education, a realignment of the tax structure, and/or a broadening of the eligi-bility base for public expenditure programmes. With respect to the latter alternative, eligibility forpublic subsidies to young people might well be expanded so as to embrace all young people - not onlythose who go on to college but also those who opt for alternative ways of expanding their earning power,such as apprenticeship or on-the-job training, or even investments in businesses, In any case, it isclear that whatever the degree to which our current higher education programmes are rooted in thesearch for equality of opportunity, the results still leave much to be desired,

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OECD 28.4615 1971

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